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    <title>Pinboard (cshalizi)</title>
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    <description>recent bookmarks from cshalizi</description>
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	<rdf:li rdf:resource="https://www.nber.org/papers/w32754"/>
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	<rdf:li rdf:resource="https://arxiv.org/abs/2008.11477"/>
	<rdf:li rdf:resource="http://www.mit.edu/~mitter/publications/100_variational_approach_SIAM.pdf"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/1807.08351"/>
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	<rdf:li rdf:resource="https://arxiv.org/abs/1909.10287"/>
	<rdf:li rdf:resource="https://www.cambridge.org/9781316649466"/>
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	<rdf:li rdf:resource="http://krugman.blogs.nytimes.com/2012/07/11/filters-and-full-employment-not-wonkish-really/"/>
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	<rdf:li rdf:resource="http://www.stat.tamu.edu/~eparzen/InferenceRKHS.pdf"/>
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	<rdf:li rdf:resource="http://www.ec-securehost.com/SIAM/OT107.html"/>
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  </channel><item rdf:about="https://arxiv.org/abs/2404.04870">
    <title>[2404.04870] Signal-noise separation using unsupervised reservoir computing</title>
    <dc:date>2024-12-11T16:11:08+00:00</dc:date>
    <link>https://arxiv.org/abs/2404.04870</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Removing noise from a signal without knowing the characteristics of the noise is a challenging task. This paper introduces a signal-noise separation method based on time series prediction. We use Reservoir Computing (RC) to extract the maximum portion of "predictable information" from a given signal. Reproducing the deterministic component of the signal using RC, we estimate the noise distribution from the difference between the original signal and reconstructed one. The method is based on a machine learning approach and requires no prior knowledge of either the deterministic signal or the noise distribution. It provides a way to identify additivity/multiplicativity of noise and to estimate the signal-to-noise ratio (SNR) indirectly. The method works successfully for combinations of various signal and noise, including chaotic signal and highly oscillating sinusoidal signal which are corrupted by non-Gaussian additive/ multiplicative noise. The separation performances are robust and notably outstanding for signals with strong noise, even for those with negative SNR."]]></description>
<dc:subject>to:NB filtering prediction to_read</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:52fa75dc577b/</dc:identifier>
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	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:filtering"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:prediction"/>
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<item rdf:about="https://www.nber.org/papers/w32754">
    <title>Filtering with Limited Information | NBER</title>
    <dc:date>2024-11-06T19:54:03+00:00</dc:date>
    <link>https://www.nber.org/papers/w32754</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We propose a new tool to filter non-linear dynamic models that does not require the researcher to specify the model fully and can be implemented without solving the model. If two conditions are satisfied, we can use a flexible statistical model and a known measurement equation to back out the hidden states of the dynamic model. The first condition is that the state is sufficiently volatile or persistent to be recoverable. The second condition requires the possibly non-linear measurement to be sufficiently smooth and to map uniquely to the state absent measurement error. We illustrate the method through various simulation studies and an empirical application to a sudden stops model applied to Mexican data."]]></description>
<dc:subject>filtering state_estimation to_read in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:39bd0cd07ac2/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:filtering"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:state_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_read"/>
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<item rdf:about="https://epubs.siam.org/doi/10.1137/100799666">
    <title>A Fresh Look at the Kalman Filter | SIAM Review</title>
    <dc:date>2024-05-22T19:11:32+00:00</dc:date>
    <link>https://epubs.siam.org/doi/10.1137/100799666</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["In this paper, we discuss the Kalman filter for state estimation in noisy linear discrete-time dynamical systems. We give an overview of its history, its mathematical and statistical formulations, and its use in applications. We describe a novel derivation of the Kalman filter using Newton's method for root finding. This approach is quite general as it can also be used to derive a number of variations of the Kalman filter, including recursive estimators for both prediction and smoothing, estimators with fading memory, and the extended Kalman filter for nonlinear systems."]]></description>
<dc:subject>filtering to_teach:data_over_space_and_time to_read in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:dda505c16685/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:filtering"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_teach:data_over_space_and_time"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
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<item rdf:about="https://arxiv.org/abs/2105.04912">
    <title>[2105.04912] On Unbiased Score Estimation for Partially Observed Diffusions</title>
    <dc:date>2021-05-12T18:31:32+00:00</dc:date>
    <link>https://arxiv.org/abs/2105.04912</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We consider the problem of statistical inference for a class of partially-observed diffusion processes, with discretely-observed data and finite-dimensional parameters. We construct unbiased estimators of the score function, i.e. the gradient of the log-likelihood function with respect to parameters, with no time-discretization bias. These estimators can be straightforwardly employed within stochastic gradient methods to perform maximum likelihood estimation or Bayesian inference. As our proposed methodology only requires access to a time-discretization scheme such as the Euler-Maruyama method, it is applicable to a wide class of diffusion processes and observation models. Our approach is based on a representation of the score as a smoothing expectation using Girsanov theorem, and a novel adaptation of the randomization schemes developed in Mcleish [2011], Rhee and Glynn [2015], Jacob et al. [2020a]. This allows one to remove the time-discretization bias and burn-in bias when computing smoothing expectations using the conditional particle filter of Andrieu et al. [2010]. Central to our approach is the development of new couplings of multiple conditional particle filters. We prove under assumptions that our estimators are unbiased and have finite variance. The methodology is illustrated on several challenging applications from population ecology and neuroscience."]]></description>
<dc:subject>to:NB statistical_inference_for_stochastic_processes state-space_models stochastic_differential_equations filtering</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:b23596cf3c5c/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistical_inference_for_stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:state-space_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_differential_equations"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:filtering"/>
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<item rdf:about="https://arxiv.org/abs/2104.04773">
    <title>[2104.04773] Particle representation for the solution of the filtering problem. Application to the error expansion of filtering discretizations</title>
    <dc:date>2021-04-14T14:45:56+00:00</dc:date>
    <link>https://arxiv.org/abs/2104.04773</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We introduce a weighted particle representation for the solution of the filtering problem based on a suitably chosen variation of the classical de Finetti theorem. This representation has important theoretical and numerical applications. In this paper, we explore some of its theoretical consequences. The first is to deduce the equations satisfied by the solution of the filtering problem in three different frameworks: the signal independent Brownian measurement noise model, the spatial observations with additive white noise model and the cluster detection model in spatial point processes. Secondly we use the representation to show that a suitably chosen filtering discretisation converges to the filtering solution. Thirdly we study the leading error coefficient for the discretisation. We show that it satisfies a stochastic partial differential equation by exploiting the weighted particle representation for both the approximation and the limiting filtering solution."]]></description>
<dc:subject>to:NB filtering particle_filters convergence_of_stochastic_processes kurtz.thomas_g.</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:317a45df0a39/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:filtering"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:particle_filters"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:convergence_of_stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:kurtz.thomas_g."/>
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</item>
<item rdf:about="https://arxiv.org/abs/1610.00195">
    <title>[1610.00195] Penalized Ensemble Kalman Filters for High Dimensional Non-linear Systems</title>
    <dc:date>2021-03-17T21:14:06+00:00</dc:date>
    <link>https://arxiv.org/abs/1610.00195</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["The ensemble Kalman filter (EnKF) is a data assimilation technique that uses an ensemble of models, updated with data, to track the time evolution of a usually non-linear system. It does so by using an empirical approximation to the well-known Kalman filter. However, its performance can suffer when the ensemble size is smaller than the state space, as is often necessary for computationally burdensome models. This scenario means that the empirical estimate of the state covariance is not full rank and possibly quite noisy. To solve this problem in this high dimensional regime, we propose a computationally fast and easy to implement algorithm called the penalized ensemble Kalman filter (PEnKF). Under certain conditions, it can be theoretically proven that the PEnKF will be accurate (the estimation error will converge to zero) despite having fewer ensemble members than state dimensions. Further, as contrasted to localization methods, the proposed approach learns the covariance structure associated with the dynamical system. These theoretical results are supported with simulations of several non-linear and high dimensional systems."]]></description>
<dc:subject>filtering state_estimation statistics time_series hero.alfred_o. in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:a3d04f3073a8/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:filtering"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:state_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
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	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:hero.alfred_o."/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
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</item>
<item rdf:about="https://arxiv.org/abs/2007.08974">
    <title>[2007.08974] Inference for partially observed epidemic dynamics guided by Kalman filtering techniques</title>
    <dc:date>2021-01-19T20:05:22+00:00</dc:date>
    <link>https://arxiv.org/abs/2007.08974</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Despite the recent development of methods dealing with partially observed epidemics (unobserved model coordinates, discrete and noisy outbreak data), some limitations remain in practice, mainly related to the amount of augmented data and the adjustment of numerous tuning parameters. In particular, coordinates of dynamic epidemic models being coupled, the presence of unobserved ones leads to a statistically difficult problem. Our aim is to propose a generic inference method easily practicable and able to tackle these issues. Using the properties of epidemics in large populations, we first build a two-layer model. Through a diffusion based approach, we obtain a Gaussian approximation of the epidemic density-dependent Markovian jump process, which represents the state model. The observational model consists in noisy observations of the observed coordinates and is approximated by Gaussian distributions. Then, we develop an inference method based on an approximate likelihood using Kalman filter recursions to estimate parameters of both state and observational models. Performances of estimators of key model parameters are assessed on simulated data of SIR epidemic dynamics for different scenarios with respect to the population size and the number of observations, and compared with those obtained by the currently largely used method of maximum iterated filtering (MIF). Finally, we apply our method on a real data set of influenza outbreak in a North England boarding school in 1978."]]></description>
<dc:subject>to:NB epidemic_models filtering state_estimation to_teach:data_over_space_and_time</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:bbe857c63d82/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:epidemic_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:filtering"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:state_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_teach:data_over_space_and_time"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2101.03957">
    <title>[2101.03957] Pathwise approximations for the solution of the non-linear filtering problem</title>
    <dc:date>2021-01-12T22:37:56+00:00</dc:date>
    <link>https://arxiv.org/abs/2101.03957</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We consider high order approximations of the solution of the stochastic filtering problem, derive their pathwise representation in the spirit of the earlier work of Clark and Davis and prove their robustness property. In particular, we show that the high order discretised filtering functionals can be represented by Lipschitz continuous functions defined on the observation path space. This property is important from the practical point of view as it is in fact the pathwise version of the filtering functional that is sought in numerical applications. Moreover, the pathwise viewpoint will be a stepping stone into the rigorous development of machine learning methods for the filtering problem. This work is a continuation of a recent work by two of the authors where a discretisation of the solution of the filtering problem of arbitrary order has been established. We expand the previous work by showing that robust approximations can be derived from the discretisations therein."]]></description>
<dc:subject>to:NB filtering stochastic_processes</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:c636d1c07f8d/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:filtering"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2008.11477">
    <title>[2008.11477] Bellman filtering for state-space models</title>
    <dc:date>2021-01-12T22:36:48+00:00</dc:date>
    <link>https://arxiv.org/abs/2008.11477</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["This article presents a filter for state-space models based on Bellman's dynamic programming principle applied to the mode estimator. The proposed Bellman filter (BF) generalises the Kalman filter (KF) including its extended and iterated versions, while remaining equally inexpensive computationally. The BF is also (unlike the KF) robust under heavy-tailed observation noise and applicable to a wider range of (nonlinear and non-Gaussian) models, involving e.g. count, intensity, duration, volatility and dependence. (Hyper)parameters are estimated by numerically maximising a BF-implied log-likelihood decomposition, which is an alternative to the classic prediction-error decomposition for linear Gaussian models. Simulation studies reveal that the BF performs on par with (or even outperforms) state-of-the-art importance-sampling techniques, while requiring a fraction of the computational cost, being straightforward to implement and offering full scalability to higher dimensional state spaces."]]></description>
<dc:subject>state_estimation filtering optimization state-space_models in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:eb0e619a36af/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:state_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:filtering"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:optimization"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:state-space_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
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</item>
<item rdf:about="http://www.mit.edu/~mitter/publications/100_variational_approach_SIAM.pdf">
    <title>A Variational Approach to Nonlinear Estimation</title>
    <dc:date>2020-12-15T15:12:36+00:00</dc:date>
    <link>http://www.mit.edu/~mitter/publications/100_variational_approach_SIAM.pdf</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We consider estimation problems, in which the estimand, X, and observation, Y ,
take values in measurable spaces. Regular conditional versions of the forward and inverse Bayes
formula are shown to have dual variational characterizations involving the minimization of apparent
information and the maximization of compatible information. These both have natural informationtheoretic interpretations, according to which Bayes’ formula and its inverse are optimal information
processors. The variational characterization of the forward formula has the same form as that of Gibbs
measures in statistical mechanics. The special case in which X and Y are diffusion processes governed
by stochastic differential equations is examined in detail. The minimization of apparent information
can then be formulated as a stochastic optimal control problem, with cost that is quadratic in both
the control and observation fit. The dual problem can be formulated in terms of infinite-dimensional
deterministic optimal control. Local versions of the variational characterizations are developed which
quantify information flow in the estimators. In this context, the information conserving property of
Bayesian estimators coincides with the Davis–Varaiya martingale stochastic dynamic programming
principle."]]></description>
<dc:subject>to:NB to_read filtering bayesianism via:mraginsky</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:c6f424e7e845/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:filtering"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:bayesianism"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:via:mraginsky"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1807.08351">
    <title>[1807.08351] Data Assimilation: The Schrödinger Perspective</title>
    <dc:date>2020-07-22T15:01:11+00:00</dc:date>
    <link>https://arxiv.org/abs/1807.08351</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Data assimilation addresses the general problem of how to combine model-based predictions with partial and noisy observations of the process in an optimal manner. This survey focuses on sequential data assimilation techniques using probabilistic particle-based algorithms. In addition to surveying recent developments for discrete- and continuous-time data assimilation, both in terms of mathematical foundations and algorithmic implementations, we also provide a unifying framework from the perspective of coupling of measures, and Schrödinger's boundary value problem for stochastic processes in particular."]]></description>
<dc:subject>state_estimation particle_filters time_series spatio-temporal_statistics to_read to_teach:data_over_space_and_time filtering in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:879ef3d9527d/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:state_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:particle_filters"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:time_series"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:spatio-temporal_statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_teach:data_over_space_and_time"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:filtering"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://www.cambridge.org/us/academic/subjects/engineering/control-systems-and-optimization/stochastic-dynamics-filtering-and-optimization?format=HB">
    <title>Stochastic dynamics filtering and optimization | Control systems and optimization | Cambridge University Press</title>
    <dc:date>2020-01-09T17:57:40+00:00</dc:date>
    <link>https://www.cambridge.org/us/academic/subjects/engineering/control-systems-and-optimization/stochastic-dynamics-filtering-and-optimization?format=HB</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Targeted at graduate students, researchers and practitioners in the field of science and engineering, this book gives a self-contained introduction to a measure-theoretic framework in laying out the definitions and basic concepts of random variables and stochastic diffusion processes. It then continues to weave into a framework of several practical tools and applications involving stochastic dynamical systems. These include tools for the numerical integration of such dynamical systems, nonlinear stochastic filtering and generalized Bayesian update theories for solving inverse problems and a new stochastic search technique for treating a broad class of non-convex optimization problems. MATLAB® codes for all the applications are uploaded on the companion website."]]></description>
<dc:subject>books:noted optimization filtering state_estimation stochastic_processes state-space_models re:almost_none books:suggest_to_library in_NB downloaded</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:30fbcfbf0054/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:books:noted"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:optimization"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:filtering"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:state_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:state-space_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:almost_none"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:books:suggest_to_library"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:downloaded"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1909.10287">
    <title>[1909.10287] Mean Field approach to stochastic control with partial information</title>
    <dc:date>2019-09-26T18:03:50+00:00</dc:date>
    <link>https://arxiv.org/abs/1909.10287</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["The classical stochastic control problem under partial information can be formulated as a control problem for Zakai equation, whose solution is the unnormalized conditional probability distribution of the state of the system, which is not directly accessible. Zakai equation is a stochastic Fokker-Planck equation. Therefore, the problem to be solved is similar to that met in Mean Field Control theory. Since Mean Field Control theory is much posterior to the development of Stochastic Control with partial information, the tools, techniques, and concepts obtained in the last decade, for Mean Field Games and Mean field type Control theory, have not been used for the control of Zakai equation. It is the objective of this work to connect the two theories. Not only, we get the power of new tools, but also we get new insights for the problem of stochastic control with partial information. For mean field theory, we get new interesting applications, but also new problems. Indeed, Mean Field Control Theory leads to very complex equations, like the Master equation, which is a nonlinear infinite dimensional P.D.E., for which general theorems are hardly available, although active research in this direction is performed. Direct methods are useful to obtain regularity results. We will develop in detail the linear quadratic regulator problem, but because we cannot just consider the Gaussian case, well-known results, as the separation principle is not available. An interesting and important result is available in the literature, due to A. Makowsky. It describes the solution of Zakai equation for linear systems with general initial condition (non-gaussian). Curiously, this result had not been exploited for the control aspect, in the literature. We show that the separation principle can be extended for quadratic pay-off functionals, but the Kalman filter is much more complex than in the gaussian case."]]></description>
<dc:subject>to:NB control_theory_and_control_engineering stochastic_processes filtering state_estimation state-space_models</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:88d010408e74/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:control_theory_and_control_engineering"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:filtering"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:state_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:state-space_models"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://www.cambridge.org/9781316649466">
    <title>Applied stochastic differential equations</title>
    <dc:date>2019-05-14T15:49:04+00:00</dc:date>
    <link>https://www.cambridge.org/9781316649466</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Stochastic differential equations are differential equations whose solutions are stochastic processes. They exhibit appealing mathematical properties that are useful in modeling uncertainties and noisy phenomena in many disciplines. This book is motivated by applications of stochastic differential equations in target tracking and medical technology and, in particular, their use in methodologies such as filtering, smoothing, parameter estimation, and machine learning. It builds an intuitive hands-on understanding of what stochastic differential equations are all about, but also covers the essentials of Itô calculus, the central theorems in the field, and such approximation schemes as stochastic Runge–Kutta. Greater emphasis is given to solution methods than to analysis of theoretical properties of the equations. The book's practical approach assumes only prior understanding of ordinary differential equations. The numerous worked examples and end-of-chapter exercises include application-driven derivations and computational assignments. MATLAB/Octave source code is available for download, promoting hands-on work with the methods."

--- PDF from the authors somewhere.]]></description>
<dc:subject>to:NB books:noted stochastic_differential_equations stochastic_processes filtering time_series statistical_inference_for_stochastic_processes</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:be7b53a609b6/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:books:noted"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_differential_equations"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:filtering"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:time_series"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistical_inference_for_stochastic_processes"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://onlinelibrary.wiley.com/doi/10.1111/jtsa.12430">
    <title>On the Sensitivity of Granger Causality to Errors‐In‐Variables, Linear Transformations and Subsampling - Anderson - - Journal of Time Series Analysis - Wiley Online Library</title>
    <dc:date>2018-09-30T14:48:10+00:00</dc:date>
    <link>https://onlinelibrary.wiley.com/doi/10.1111/jtsa.12430</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["This article studies the sensitivity of Granger causality to the addition of noise, the introduction of subsampling, and the application of causal invertible filters to weakly stationary processes. Using canonical spectral factors and Wold decompositions, we give general conditions under which additive noise or filtering distorts Granger‐causal properties by inducing (spurious) Granger causality, as well as conditions under which it does not. For the errors‐in‐variables case, we give a continuity result, which implies that: a ‘small’ noise‐to‐signal ratio entails ‘small’ distortions in Granger causality. On filtering, we give general necessary and sufficient conditions under which ‘spurious’ causal relations between (vector) time series are not induced by linear transformations of the variables involved. This also yields transformations (or filters) which can eliminate Granger causality from one vector to another one. In a number of cases, we clarify results in the existing literature, with a number of calculations streamlining some existing approaches."]]></description>
<dc:subject>time_series prediction granger_causality in_NB filtering</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:76bd984e3518/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:time_series"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:prediction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:granger_causality"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:filtering"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1606.08650">
    <title>[1606.08650] Approximate Smoothing and Parameter Estimation in High-Dimensional State-Space Models</title>
    <dc:date>2016-09-07T14:54:27+00:00</dc:date>
    <link>http://arxiv.org/abs/1606.08650</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We present approximate algorithms for performing smoothing in a class of high-dimensional state-space models via sequential Monte Carlo methods ("particle filters"). In high dimensions, a prohibitively large number of Monte Carlo samples ("particles") -- growing exponentially in the dimension of the state space -- is usually required to obtain a useful smoother. Using blocking strategies as in Rebeschini and Van Handel (2015) (and earlier pioneering work on blocking), we exploit the spatial ergodicity properties of the model to circumvent this curse of dimensionality. We thus obtain approximate smoothers that can be computed recursively in time and in parallel in space. First, we show that the bias of our blocked smoother is bounded uniformly in the time horizon and in the model dimension. We then approximate the blocked smoother with particles and derive the asymptotic variance of idealised versions of our blocked particle smoother to show that variance is no longer adversely effected by the dimension of the model. Finally, we employ our method to successfully perform maximum-likelihood estimation via stochastic gradient-ascent and stochastic expectation--maximisation algorithms in a 100-dimensional state-space model."]]></description>
<dc:subject>to:NB particle_filters time_series statistical_inference_for_stochastic_processes filtering stochastic_processes state-space_models high-dimensional_statistics singh.sumeetpal_s. statistics re:fitness_sampling</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:a76b4d887144/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:particle_filters"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:time_series"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistical_inference_for_stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:filtering"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:state-space_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:high-dimensional_statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:singh.sumeetpal_s."/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:fitness_sampling"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1301.6585">
    <title>[1301.6585] Can local particle filters beat the curse of dimensionality?</title>
    <dc:date>2016-09-07T14:50:14+00:00</dc:date>
    <link>http://arxiv.org/abs/1301.6585</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["The discovery of particle filtering methods has enabled the use of nonlinear filtering in a wide array of applications. Unfortunately, the approximation error of particle filters typically grows exponentially in the dimension of the underlying model. This phenomenon has rendered particle filters of limited use in complex data assimilation problems. In this paper, we argue that it is often possible, at least in principle, to develop local particle filtering algorithms whose approximation error is dimension-free. The key to such developments is the decay of correlations property, which is a spatial counterpart of the much better understood stability property of nonlinear filters. For the simplest possible algorithm of this type, our results provide under suitable assumptions an approximation error bound that is uniform both in time and in the model dimension. More broadly, our results provide a framework for the investigation of filtering problems and algorithms in high dimension."]]></description>
<dc:subject>to:NB filtering van_handel.ramon particle_filters stochastic_processes high-dimensional_statistics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:bcc06551da52/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:filtering"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:van_handel.ramon"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:particle_filters"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:high-dimensional_statistics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://projecteuclid.org/euclid.aos/1176348259">
    <title>Thomas-Agnan : Spline Functions and Stochastic Filtering</title>
    <dc:date>2016-04-16T15:13:50+00:00</dc:date>
    <link>http://projecteuclid.org/euclid.aos/1176348259</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Some relationships have been established between unbiased linear predictors of processes, in signal and noise models, minimizing the predictive mean square error and some smoothing spline functions. We construct a new family of multidimensional splines adapted to the prediction of locally homogeneous random fields, whose "m-spectral measure" (to be defined) is absolutely continuous with respect to Lebesgue measure and satisfies some minor assumptions. By considering partial splines, one may include an arbitrary drift in the signal. This type of correspondence underlines the potentialities of cross-fertilization between statistics and the numerical techniques in approximation theory."]]></description>
<dc:subject>to:NB splines prediction filtering statistics hilbert_space fourier_analysis random_fields have_read</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:f733830bbdcd/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:splines"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:prediction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:filtering"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:hilbert_space"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:fourier_analysis"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:random_fields"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:have_read"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1601.05033">
    <title>[1601.05033] Optimal tracking for dynamical systems</title>
    <dc:date>2016-02-09T02:56:10+00:00</dc:date>
    <link>http://arxiv.org/abs/1601.05033</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We study the limiting behavior of the average per-state cost when trajectories of a topological dynamical system are used to track a trajectory from an observed ergodic system. We establish a variational characterization of the limiting average cost in terms of dynamically invariant couplings, also known as joinings, of the two dynamical systems, and we show that the set of optimal joinings is convex and compact in the weak topology. Using these results, we establish a general convergence theorem for the limiting behavior of statistical inference procedures based on optimal tracking. The setting considered here is general enough to encompass traditional statistical problems with weakly dependent, real-valued observations. As applications of the general inference result, we consider the consistency of regression estimation under ergodic sampling and of system identification from quantized observations."]]></description>
<dc:subject>to:NB dynamical_systems stochastic_processes statistical_inference_for_stochastic_processes filtering nobel.andrew</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:a7a072c88de4/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dynamical_systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistical_inference_for_stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:filtering"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:nobel.andrew"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://projecteuclid.org/euclid.bj/1411134448">
    <title>Crisan , Míguez : Particle-kernel estimation of the filter density in state-space models</title>
    <dc:date>2015-01-24T14:11:26+00:00</dc:date>
    <link>http://projecteuclid.org/euclid.bj/1411134448</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Sequential Monte Carlo (SMC) methods, also known as particle filters, are simulation-based recursive algorithms for the approximation of the a posteriori probability measures generated by state-space dynamical models. At any given time t, a SMC method produces a set of samples over the state space of the system of interest (often termed “particles”) that is used to build a discrete and random approximation of the posterior probability distribution of the state variables, conditional on a sequence of available observations. One potential application of the methodology is the estimation of the densities associated to the sequence of a posteriori distributions. While practitioners have rather freely applied such density approximations in the past, the issue has received less attention from a theoretical perspective. In this paper, we address the problem of constructing kernel-based estimates of the posterior probability density function and its derivatives, and obtain asymptotic convergence results for the estimation errors. In particular, we find convergence rates for the approximation errors that hold uniformly on the state space and guarantee that the error vanishes almost surely as the number of particles in the filter grows. Based on this uniform convergence result, we first show how to build continuous measures that converge almost surely (with known rate) toward the posterior measure and then address a few applications. The latter include maximum a posteriori estimation of the system state using the approximate derivatives of the posterior density and the approximation of functionals of it, for example, Shannon’s entropy."]]></description>
<dc:subject>particle_filters density_estimation filtering state_estimation state-space_models statistics computational_statistics in_NB kernel_smoothing</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:77a953685926/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:particle_filters"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:density_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:filtering"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:state_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:state-space_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:computational_statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:kernel_smoothing"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://projecteuclid.org/euclid.bams/1183527586">
    <title>Masani : Wiener's contributions to generalized harmonic analysis, prediction theory and filter theory</title>
    <dc:date>2014-10-14T20:03:37+00:00</dc:date>
    <link>http://projecteuclid.org/euclid.bams/1183527586</link>
    <dc:creator>cshalizi</dc:creator><dc:subject>have_read wiener.norbert mathematics fourier_analysis time_series prediction filtering stochastic_processes in_NB to:blog</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:0f8263c3c22e/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:have_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:wiener.norbert"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:mathematics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:fourier_analysis"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:time_series"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:prediction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:filtering"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:blog"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1402.1253">
    <title>[1402.1253] An Ensemble Kushner-Stratonovich (EnKS) Nonlinear Filter: Additive Particle Updates in Non-Iterative and Iterative Forms</title>
    <dc:date>2014-03-08T22:41:43+00:00</dc:date>
    <link>http://arxiv.org/abs/1402.1253</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Despite the cheap availability of computing resources enabling faster Monte Carlo simulations, the potential benefits of particle filtering in revealing accurate statistical information on the imprecisely known model parameters or modeling errors of dynamical systems, based on limited time series data, have not been quite realized. A major numerical bottleneck precipitating this under-performance, especially for higher dimensional systems, is the progressive particle impoverishment owing to weight collapse and the aim of the current work is to address this problem by replacing weight-based updates through additive ones. Thus, in the context of nonlinear filtering problems, a novel additive particle update scheme, in its non-iterative and iterative forms, is proposed based on manipulations of the innovation integral in the governing Kushner-Stratonovich equation. Numerical evidence for the identification of nonlinear and large dimensional dynamical systems indicates a substantively superior performance of the non- iterative version of the EnKS vis-\`a-vis most existing filters. The costlier iterative version, though conceptually elegant, mostly appears to effect a marginal improvement in the reconstruction accuracy over its non-iterative counterpart. Prominent in the reported numerical comparisons are variants of the Ensemble Kalman Filter (EnKF) that also use additive updates, albeit with many inherent limitations of a Kalman filter."]]></description>
<dc:subject>to:NB particle_filters filtering statistics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:66385402463f/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:particle_filters"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:filtering"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1402.3466">
    <title>[1402.3466] Kernel density estimates in particle filter</title>
    <dc:date>2014-03-08T22:39:09+00:00</dc:date>
    <link>http://arxiv.org/abs/1402.3466</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["The paper deals with kernel estimates of densities of filtering distributions in the particle filter. The convergence of the estimates is investigated by means of Fourier analysis. It is shown that the estimates converge to theoretical filtering densities in the mean integrated squared error under a certain assumption on the Sobolev character of the filtering densities. A sufficient condition is presented for the persistence of this Sobolev character over time."]]></description>
<dc:subject>to:NB density_estimation particle_filters filtering statistics kernel_smoothing</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:dfbfe8acfb74/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:density_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:particle_filters"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:filtering"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:kernel_smoothing"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1401.6450">
    <title>[1401.6450] Phase Transitions in Nonlinear Filtering</title>
    <dc:date>2014-02-22T03:40:42+00:00</dc:date>
    <link>http://arxiv.org/abs/1401.6450</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["It has been established under very general conditions that the ergodic properties of Markov processes are inherited by their conditional distributions given partial information. While the existing theory provides a rather complete picture of classical filtering models, many infinite-dimensional problems are outside its scope. Far from being a technical issue, the infinite-dimensional setting gives rise to surprising phenomena and new questions in filtering theory. The aim of this paper is to discuss some elementary examples, conjectures, and general theory that arise in this setting, and to highlight connections with problems in statistical mechanics and ergodic theory. In particular, we exhibit a simple example of a uniformly ergodic model in which ergodicity of the filter undergoes a phase transition, and we develop some qualitative understanding as to when such phenomena can and cannot occur. We also discuss closely related problems in the setting of conditional Markov random fields."]]></description>
<dc:subject>to:NB filtering phase_transitions stochastic_processes markov_models van_handel.ramon</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:72f9fd426c13/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:filtering"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:phase_transitions"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:markov_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:van_handel.ramon"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://projecteuclid.org/euclid.aos/1387313393">
    <title>Chan , Lai : A general theory of particle filters in hidden Markov models and some applications</title>
    <dc:date>2014-02-20T22:21:27+00:00</dc:date>
    <link>http://projecteuclid.org/euclid.aos/1387313393</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["By making use of martingale representations, we derive the asymptotic normality of particle filters in hidden Markov models and a relatively simple formula for their asymptotic variances. Although repeated resamplings result in complicated dependence among the sample paths, the asymptotic variance formula and martingale representations lead to consistent estimates of the standard errors of the particle filter estimates of the hidden states."]]></description>
<dc:subject>particle_filters filtering state_estimation martingales statistical_inference_for_stochastic_processes statistics state-space_models markov_models stochastic_processes in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:76bc97fcf610/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:particle_filters"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:filtering"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:state_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:martingales"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistical_inference_for_stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:state-space_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:markov_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1209.0633">
    <title>[1209.0633] Nonparametric regression on hidden phi-mixing variables: identifiability and consistency of a pseudo-likelihood based estimation procedure</title>
    <dc:date>2014-02-20T01:04:28+00:00</dc:date>
    <link>http://arxiv.org/abs/1209.0633</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["This paper outlines a new nonparametric estimation procedure for unobserved phi-mixing processes. It is assumed that the only information on the stationary hidden states (Xk) is given by the process (Yk), where Yk is a noisy observation of f(Xk). The paper introduces a maximum pseudo-likelihood procedure to estimate the function f and the distribution of the hidden states using blocks of observations of length b. The identifiability of the model is studied in the particular cases b=1 and b=2. The consistency of the estimators of f and of the distribution of the hidden states as the number of observations grows to infinity is established."]]></description>
<dc:subject>to:NB statistical_inference_for_stochastic_processes time_series filtering statistics mixing</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:4a6c43d17081/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistical_inference_for_stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:time_series"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:filtering"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:mixing"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://projecteuclid.org/DPubS?service=UI&amp;version=1.0&amp;verb=Display&amp;handle=euclid.bj/1386078601">
    <title>Dubarry , Le Corff : Non-asymptotic deviation inequalities for smoothed additive functionals in nonlinear state-space models</title>
    <dc:date>2013-12-03T15:56:43+00:00</dc:date>
    <link>http://projecteuclid.org/DPubS?service=UI&amp;version=1.0&amp;verb=Display&amp;handle=euclid.bj/1386078601</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["The approximation of fixed-interval smoothing distributions is a key issue in inference for general state-space hidden Markov models (HMM). This contribution establishes non-asymptotic bounds for the Forward Filtering Backward Smoothing (FFBS) and the Forward Filtering Backward Simulation (FFBSi) estimators of fixed-interval smoothing functionals. We show that the rate of convergence of the Lq-mean errors of both methods depends on the number of observations T and the number of particles N only through the ratio T/N for additive functionals. In the case of the FFBS, this improves recent results providing bounds depending on T/N‾‾√."]]></description>
<dc:subject>filtering state_estimation state-space_models markov_models stochastic_processes deviation_inequalities statistical_inference_for_stochastic_processes statistics in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:2c1ce9d96796/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:filtering"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:state_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:state-space_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:markov_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:deviation_inequalities"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistical_inference_for_stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1310.5951">
    <title>[1310.5951] A Tractable State-Space Model for the Riemannian Manifold of Symmetric Positive Definite Matrices</title>
    <dc:date>2013-10-23T19:53:05+00:00</dc:date>
    <link>http://arxiv.org/abs/1310.5951</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Many tools exist to filter, smooth, and predict latent quantities when state-space modeling in ℝn. However, there are scenarios, like tracking an object in a video or tracking a covariance matrix of financial assets returns, when one would like to do state-space modeling on a Riemannian manifold that is not a vector space. Most work addressing manifold-valued state-space models has focused on adapting methods for filtering on ℝn to filtering on Riemannian manifolds. Less attention has been paid to other aspects of state-space inference, which tend to be more challenging. To that end, we present a parsimonious state-space model whose observations and latent states take values on the Riemannian manifold of symmetric positive definite matrices and show how to forward filter, backward sample, and infer the parameters that govern the dynamics of the latent states, providing a complete set of tools for state-space inference in this domain."]]></description>
<dc:subject>to:NB state-space_models statistics_on_manifolds filtering statistics carvalho.carlos_m.</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:99985bc07968/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:state-space_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics_on_manifolds"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:filtering"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:carvalho.carlos_m."/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://projecteuclid.org/euclid.bj/1377612857">
    <title>Künsch : Particle filters</title>
    <dc:date>2013-09-04T21:07:36+00:00</dc:date>
    <link>http://projecteuclid.org/euclid.bj/1377612857</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["This is a short review of Monte Carlo methods for approximating filter distributions in state space models. The basic algorithm and different strategies to reduce imbalance of the weights are discussed. Finally, methods for more difficult problems like smoothing and parameter estimation and applications outside the state space model context are presented."]]></description>
<dc:subject>particle_filters statistical_inference_for_stochastic_processes time_series filtering statistics in_NB have_read</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:0e462fe36e84/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:particle_filters"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistical_inference_for_stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:time_series"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:filtering"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:have_read"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://www.pnas.org/content/110/31/12535.abstract">
    <title>Empirical intrinsic geometry for nonlinear modeling and time series filtering</title>
    <dc:date>2013-09-03T12:26:55+00:00</dc:date>
    <link>http://www.pnas.org/content/110/31/12535.abstract</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["In this paper, we present a method for time series analysis based on empirical intrinsic geometry (EIG). EIG enables one to reveal the low-dimensional parametric manifold as well as to infer the underlying dynamics of high-dimensional time series. By incorporating concepts of information geometry, this method extends existing geometric analysis tools to support stochastic settings and parametrizes the geometry of empirical distributions. However, the statistical models are not required as priors; hence, EIG may be applied to a wide range of real signals without existing definitive models. We show that the inferred model is noise-resilient and invariant under different observation and instrumental modalities. In addition, we show that it can be extended efficiently to newly acquired measurements in a sequential manner. These two advantages enable us to revisit the Bayesian approach and incorporate empirical dynamics and intrinsic geometry into a nonlinear filtering framework. We show applications to nonlinear and non-Gaussian tracking problems as well as to acoustic signal localization."

- Contributed papers in PNAS are however always somewhat dubious.]]></description>
<dc:subject>time_series prediction manifold_learning dimension_reduction statistics machine_learning to_read filtering state_estimation information_geometry entableted in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:5c5423af007e/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:time_series"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:prediction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:manifold_learning"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dimension_reduction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:machine_learning"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:filtering"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:state_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:information_geometry"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:entableted"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://www.springer.com/physics/complexity/book/978-1-4614-7217-9?cm_mmc=NBA-_-Jul-13_WEST_13201678-_-product-_-978-1-4614-7217-9&amp;otherVersion=978-1-4614-7218-6">
    <title>Predicting the Future - Completing Models of Observed Complex Systems</title>
    <dc:date>2013-07-11T20:11:13+00:00</dc:date>
    <link>http://www.springer.com/physics/complexity/book/978-1-4614-7217-9?cm_mmc=NBA-_-Jul-13_WEST_13201678-_-product-_-978-1-4614-7217-9&amp;otherVersion=978-1-4614-7218-6</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Predicting the Future: Completing Models of Observed Complex Systems provides a general framework for the discussion of model building and validation across a broad spectrum of disciplines. This is accomplished through the development of an exact path integral for use in transferring information from observations to a model of the observed system. Through many illustrative examples drawn from models in neuroscience, fluid dynamics, geosciences, and nonlinear electrical circuits, the concepts are exemplified in detail. Practical numerical methods for approximate evaluations of the path integral are explored, and their use in designing experiments and determining a model's consistency with observations is investigated.
"Using highly instructive examples, the problems of data assimilation and the means to treat them are clearly illustrated. This book will be useful for students and practitioners of physics, neuroscience, regulatory networks, meteorology and climate science, network dynamics, fluid dynamics, and other systematic investigations of complex systems."]]></description>
<dc:subject>to:NB books:noted statistical_inference_for_stochastic_processes complexity dynamical_systems filtering prediction abarbanel.henry</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:80a6a8c60d6c/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:books:noted"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistical_inference_for_stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:complexity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dynamical_systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:filtering"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:prediction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:abarbanel.henry"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1305.5797">
    <title>[1305.5797] Convergence in distribution for filtering processes associated to Hidden Markov Models with densities</title>
    <dc:date>2013-05-27T03:44:16+00:00</dc:date>
    <link>http://arxiv.org/abs/1305.5797</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["A Hidden Markov Model generates two basic stochastic processes, a Markov chain, which is hidden, and an observation sequence. The filtering process of a Hidden Markov Model is, roughly speaking, the sequence of conditional distributions of the hidden Markov chain that is obtained as new observations are received. It is well-known, that the filtering process itself, is also a Markov chain. A classical, theoretical problem is to find conditions which imply that the distributions of the filtering process converge towards a unique limit measure. This problem goes back to a paper of D Blackwell for the case when the Markov chain takes its values in a finite set and it goes back to a paper of H Kunita for the case when the state space of the Markov chain is a compact Hausdorff space. Recently due to work by F Kochman, J Reeds, P Chigansky and R van Handel, a necessary and sufficient condition for the convergence of the distributions of the filtering process has been found for the case when the state space is finite. This condition has since been generalised to the case when the state space is denumerable. In this paper we generalise some of the previous results on convergence in distribution to the case when the Markov chain and the observation sequence of a Hidden Markov Model take their values in complete separable metric spaces; it has though been necessary to assume that both the transition probability function of the Markov chain and the transition probability function that generates the observation sequence have densities."]]></description>
<dc:subject>to:NB filtering markov_models stochastic_processes state-space_models</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:dbfa83e8db55/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:filtering"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:markov_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:state-space_models"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1305.0320">
    <title>[1305.0320] MCMC for non-linear state space models using ensembles of latent sequences</title>
    <dc:date>2013-05-03T18:35:37+00:00</dc:date>
    <link>http://arxiv.org/abs/1305.0320</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Non-linear state space models are a widely-used class of models for biological, economic, and physical processes. Fitting these models to observed data is a difficult inference problem that has no straightforward solution. We take a Bayesian approach to the inference of unknown parameters of a non-linear state model; this, in turn, requires the availability of efficient Markov Chain Monte Carlo (MCMC) sampling methods for the latent (hidden) variables and model parameters. Using the ensemble technique of Neal (2010) and the embedded HMM technique of Neal (2003), we introduce a new Markov Chain Monte Carlo method for non-linear state space models. The key idea is to perform parameter updates conditional on an enormously large ensemble of latent sequences, as opposed to a single sequence, as with existing methods. We look at the performance of this ensemble method when doing Bayesian inference in the Ricker model of population dynamics. We show that for this problem, the ensemble method is vastly more efficient than a simple Metropolis method, as well as 1.9 to 12.0 times more efficient than a single-sequence embedded HMM method, when all methods are tuned appropriately. We also introduce a way of speeding up the ensemble method by performing partial backward passes to discard poor proposals at low computational cost, resulting in a final efficiency gain of 3.4 to 20.4 times over the single-sequence method."]]></description>
<dc:subject>filtering state-space_models state_estimation estimation time_series markov_models monte_carlo statistics neal.radford in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:02250f392083/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:filtering"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:state-space_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:state_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:time_series"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:markov_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:monte_carlo"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:neal.radford"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://www.jstatsoft.org/v53/i05">
    <title>cts: An R Package for Continuous Time Autoregressive Models via Kalman Filter</title>
    <dc:date>2013-04-22T17:18:22+00:00</dc:date>
    <link>http://www.jstatsoft.org/v53/i05</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We describe an R package cts for fitting a modified form of continuous time autoregressive model, which can be particularly useful with unequally sampled time series. The estimation is based on the application of the Kalman filter. The paper provides the methods and algorithms implemented in the package, including parameter estimation, spectral analysis, forecasting, model checking and Kalman smoothing. The package contains R functions which interface underlying Fortran routines. The package is applied to geophysical and medical data for illustration."]]></description>
<dc:subject>to:NB time_series R filtering state-space_models statistics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:3bfbb49c1e34/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:time_series"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:R"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:filtering"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:state-space_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1304.2986">
    <title>[1304.2986] Adaptive Piecewise Polynomial Estimation via Trend Filtering</title>
    <dc:date>2013-04-11T04:10:40+00:00</dc:date>
    <link>http://arxiv.org/abs/1304.2986</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We study trend filtering, a recently proposed tool of Kim et al. (2009) for nonparametric regression. The trend filtering estimate is defined as the minimizer of a penalized least squares criterion, in which the penalty term sums the absolute kth order discrete derivatives over the input points. Perhaps not surprisingly, trend filtering estimates appear to have the structure of kth degree spline functions, with adaptively chosen knot points (we say "appear" here as trend filtering estimates are not really functions over continuous domains, and are only defined over the discrete set of inputs). This brings to mind comparisons to other nonparametric regression tools that also produce adaptive splines; in particular, we compare trend filtering to smoothing splines, which penalize the sum of squared derivatives across input points, and to locally adaptive regression splines (Mammen & van de Geer 1997), which penalize the total variation of the kth derivative. Empirically, we discover that trend filtering estimates adapt to the local level of smoothness much better than smoothing splines, and further, they exhibit a remarkable similarity to locally adaptive regression splines. We also provide theoretical support for these empirical findings; most notably, we prove that (with the right choice of tuning parameter) the trend filtering estimate converges to the true underlying function at the minimax rate for functions whose kth derivative is of bounded variation. This is done via an asymptotic pairing of trend filtering and locally adaptive regression splines, which have already been shown to converge at the minimax rated (Mammen & van de Geer 1997). At the core of this argument is a new result tying together the fitted values of two lasso problems that share the same outcome vector, but have different predictor matrices."]]></description>
<dc:subject>to:NB filtering regression statistics splines sparsity lasso kith_and_kin have_read tibshirani.ryan</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:02f1ed0872ce/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:filtering"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:regression"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:splines"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:sparsity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:lasso"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:kith_and_kin"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:have_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:tibshirani.ryan"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://projecteuclid.org/DPubS?service=UI&amp;version=1.0&amp;verb=Display&amp;handle=euclid.ejs/1364220670">
    <title>Le Corff , Fort : Online Expectation Maximization based algorithms for inference in Hidden Markov Models</title>
    <dc:date>2013-03-25T16:52:51+00:00</dc:date>
    <link>http://projecteuclid.org/DPubS?service=UI&amp;version=1.0&amp;verb=Display&amp;handle=euclid.ejs/1364220670</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["The Expectation Maximization (EM) algorithm is a versatile tool for model parameter estimation in latent data models. When processing large data sets or data stream however, EM becomes intractable since it requires the whole data set to be available at each iteration of the algorithm. In this contribution, a new generic online EM algorithm for model parameter inference in general Hidden Markov Model is proposed. This new algorithm updates the parameter estimate after a block of observations is processed (online). The convergence of this new algorithm is established, and the rate of convergence is studied showing the impact of the block-size sequence. An averaging procedure is also proposed to improve the rate of convergence. Finally, practical illustrations are presented to highlight the performance of these algorithms in comparison to other online maximum likelihood procedures."]]></description>
<dc:subject>to:NB time_series markov_models em_algorithm estimation filtering state_estimation state-space_models statistics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:4c3bb13a47a2/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:time_series"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:markov_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:em_algorithm"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:filtering"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:state_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:state-space_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://cran.r-project.org/web/packages/mFilter/index.html">
    <title>CRAN - Package mFilter: Miscellaneous time series filters</title>
    <dc:date>2012-11-25T12:27:13+00:00</dc:date>
    <link>http://cran.r-project.org/web/packages/mFilter/index.html</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["The package implements several time series filters useful for smoothing and extracting trend and cyclical components of a time series. The routines are commonly used in economics and finance, however they should also be interest to other areas. Currently, Christiano-Fitzgerald, Baxter-King, Hodrick-Prescott, Butterworth, and trigonometric regression filters are included in the package."

May mention for the time series lectures.]]></description>
<dc:subject>statistics R time_series filtering to_teach:undergrad-ADA</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:23917d3d0151/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:R"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:time_series"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:filtering"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_teach:undergrad-ADA"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1208.2534">
    <title>[1208.2534] Locating the Source of Diffusion in Large-Scale Networks</title>
    <dc:date>2012-09-04T02:09:14+00:00</dc:date>
    <link>http://arxiv.org/abs/1208.2534</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["How can we localize the source of diffusion in a complex network? Due to the tremendous size of many real networks--such as the Internet or the human social graph--it is usually infeasible to observe the state of all nodes in a network. We show that it is fundamentally possible to estimate the location of the source from measurements collected by sparsely-placed observers. We present a strategy that is optimal for arbitrary trees, achieving maximum probability of correct localization. We describe efficient implementations with complexity O(N^{alpha}), where alpha=1 for arbitrary trees, and alpha=3 for arbitrary graphs. In the context of several case studies, we determine how localization accuracy is affected by various system parameters, including the structure of the network, the density of observers, and the number of observed cascades."

Assumptions to be examined carefully...]]></description>
<dc:subject>network_data_analysis statistics filtering in_NB re:social_networks_as_sensor_networks re:do-institutions-evolve epidemics_on_networks</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:e7d10841c46c/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:network_data_analysis"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:filtering"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:social_networks_as_sensor_networks"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:do-institutions-evolve"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:epidemics_on_networks"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://projecteuclid.org/DPubS?service=UI&amp;version=1.0&amp;verb=Display&amp;handle=euclid.aoap/1344614202">
    <title>Tong , van Handel : Ergodicity and stability of the conditional distributions of nondegenerate Markov chains</title>
    <dc:date>2012-08-10T17:53:03+00:00</dc:date>
    <link>http://projecteuclid.org/DPubS?service=UI&amp;version=1.0&amp;verb=Display&amp;handle=euclid.aoap/1344614202</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We consider a bivariate stationary Markov chain (Xn,Yn)n≥0 in a Polish state space, where only the process (Yn)n≥0 is presumed to be observable. The goal of this paper is to investigate the ergodic theory and stability properties of the measure-valued process (Πn)n≥0, where Πn is the conditional distribution of Xn given Y0,…,Yn. We show that the ergodic and stability properties of (Πn)n≥0 are inherited from the ergodicity of the unobserved process (Xn)n≥0 provided that the Markov chain (Xn,Yn)n≥0 is nondegenerate, that is, its transition kernel is equivalent to the product of independent transition kernels. Our main results generalize, subsume and in some cases correct previous results on the ergodic theory of nonlinear filters."]]></description>
<dc:subject>to_read ergodic_theory mixing filtering markov_models stochastic_processes re:almost_none van_handel.ramon in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:884d46bd9925/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:ergodic_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:mixing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:filtering"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:markov_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:almost_none"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:van_handel.ramon"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://krugman.blogs.nytimes.com/2012/07/11/filters-and-full-employment-not-wonkish-really/">
    <title>Filters and Full Employment (Not Wonkish, Really) - NYTimes.com</title>
    <dc:date>2012-07-12T01:59:57+00:00</dc:date>
    <link>http://krugman.blogs.nytimes.com/2012/07/11/filters-and-full-employment-not-wonkish-really/</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA[Dear God, are real grown-up economists confusing _the trend of realized output_ with _potential output_?  That's insane (but apparently the case - at the Fed, no less).  Well, at least explaining what's going wrong here can make a useful homework problem for undergraduate data analysis.]]></description>
<dc:subject>bad_data_analysis macroeconomics filtering time_series utter_stupidity to_teach:undergrad-ADA splines</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:251ce3c5da8e/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:bad_data_analysis"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:macroeconomics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:filtering"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:time_series"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:utter_stupidity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_teach:undergrad-ADA"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:splines"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1206.4670">
    <title>[1206.4670] State-Space Inference for Non-Linear Latent Force Models with Application to Satellite Orbit Prediction</title>
    <dc:date>2012-06-23T14:11:52+00:00</dc:date>
    <link>http://arxiv.org/abs/1206.4670</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Latent force models (LFMs) are flexible models that combine mechanistic modelling principles (i.e., physical models) with non-parametric data-driven components. Several key applications of LFMs need non-linearities, which results in analytically intractable inference. In this work we show how non-linear LFMs can be represented as non-linear white noise driven state-space models and present an efficient non-linear Kalman filtering and smoothing based method for approximate state and parameter inference. We illustrate the performance of the proposed methodology via two simulated examples, and apply it to a real-world problem of long-term prediction of GPS satellite orbits."]]></description>
<dc:subject>to:NB state-space_models nonparametrics filtering statistical_inference_for_stochastic_processes time_series machine_learning</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:bd860d658bfd/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:state-space_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:nonparametrics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:filtering"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistical_inference_for_stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:time_series"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:machine_learning"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://www.stat.tamu.edu/~eparzen/InferenceRKHS.pdf">
    <title>Statistical Inference on Time Series by RKHS Methods (Parzen, 1970)</title>
    <dc:date>2012-04-23T03:00:33+00:00</dc:date>
    <link>http://www.stat.tamu.edu/~eparzen/InferenceRKHS.pdf</link>
    <dc:creator>cshalizi</dc:creator><dc:subject>statistics statistical_inference_for_stochastic_processes time_series stochastic_processes hilbert_space filtering via:flaxman parzen.emanuel in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:d3ea8617bbaa/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistical_inference_for_stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:time_series"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:hilbert_space"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:filtering"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:via:flaxman"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:parzen.emanuel"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/0810.2123">
    <title>[0810.2123] Forgetting of the initial distribution for non-ergodic Hidden Markov Chains</title>
    <dc:date>2012-02-29T15:58:16+00:00</dc:date>
    <link>http://arxiv.org/abs/0810.2123</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["In this paper, the forgetting of the initial distribution for a non-ergodic Hidden Markov Models (HMM) is studied. A new set of conditions is proposed to establish the forgetting property of the filter, which significantly extends all the existing results. Both a pathwise-type convergence of the total variation distance of the filter started from two different initial distributions, and a convergence in expectation are considered. The results are illustrated using generic models of non-ergodic HMM and extend all the results known so far."]]></description>
<dc:subject>to:NB filtering markov_models state_estimation stochastic_processes</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:f14e6fc44982/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:filtering"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:markov_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:state_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://www.mitpressjournals.org/doi/abs/10.1162/neco.2008.10-06-351">
    <title>Online Learning with Hidden Markov Models</title>
    <dc:date>2012-02-21T04:20:08+00:00</dc:date>
    <link>http://www.mitpressjournals.org/doi/abs/10.1162/neco.2008.10-06-351</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We present an online version of the expectation-maximization (EM) algorithm for hidden Markov models (HMMs). The sufficient statistics required for parameters estimation is computed recursively with time, that is, in an online way instead of using the batch forward-backward procedure. This computational scheme is generalized to the case where the model parameters can change with time by introducing a discount factor into the recurrence relations. The resulting algorithm is equivalent to the batch EM algorithm, for appropriate discount factor and scheduling of parameters update. On the other hand, the online algorithm is able to deal with dynamic environments, i.e., when the statistics of the observed data is changing with time. The implications of the online algorithm for probabilistic modeling in neuroscience are briefly discussed."]]></description>
<dc:subject>to:NB markov_models filtering state_estimation statistics em_algorithm</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:a8088c3cdd66/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:markov_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:filtering"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:state_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:em_algorithm"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1202.2945">
    <title>[1202.2945] Sequential Monte Carlo smoothing for general state space hidden Markov models</title>
    <dc:date>2012-02-15T13:25:25+00:00</dc:date>
    <link>http://arxiv.org/abs/1202.2945</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Computing smoothing distributions, the distributions of one or more states conditional on past, present, and future observations is a recurring problem when operating on general hidden Markov models. The aim of this paper is to provide a foundation of particle-based approximation of such distributions and to analyze, in a common unifying framework, different schemes producing such approximations. In this setting, general convergence results, including exponential deviation inequalities and central limit theorems, are established. In particular, time uniform bounds on the marginal smoothing error are obtained under appropriate mixing conditions on the transition kernel of the latent chain. In addition, we propose an algorithm approximating the joint smoothing distribution at a cost that grows only linearly with the number of particles."]]></description>
<dc:subject>filtering statistics state_estimation particle_filters state-space_models stochastic_processes ergodic_theory moulines.eric douc.randal in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:51cf2f5a4960/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:filtering"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:state_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:particle_filters"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:state-space_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:ergodic_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:moulines.eric"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:douc.randal"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://ieeexplore.ieee.org/xpls/abs_all.jsp?isnumber=6094243&amp;arnumber=6015553&amp;tag=1">
    <title>IEEE Xplore - Online Learning of Noisy Data</title>
    <dc:date>2011-12-06T21:58:47+00:00</dc:date>
    <link>http://ieeexplore.ieee.org/xpls/abs_all.jsp?isnumber=6094243&amp;arnumber=6015553&amp;tag=1</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We study online learning of linear and kernel-based predictors, when individual examples are corrupted by random noise, and both examples and noise type can be chosen adversarially and change over time. We begin with the setting where some auxiliary information on the noise distribution is provided, and we wish to learn predictors with respect to the squared loss. Depending on the auxiliary information, we show how one can learn linear and kernel-based predictors, using just 1 or 2 noisy copies of each example. We then turn to discuss a general setting where virtually nothing is known about the noise distribution, and one wishes to learn with respect to general losses and using linear and kernel-based predictors. We show how this can be achieved using a random, essentially constant number of noisy copies of each example. Allowing multiple copies cannot be avoided: Indeed, we show that the setting becomes impossible when only one noisy copy of each instance can be accessed. To obtain our results we introduce several novel techniques, some of which might be of independent interest."]]></description>
<dc:subject>to:NB online_learning filtering kernel_methods machine_learning cesa-bianchi.nicolo low-regret_learning</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:07e7db063157/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:online_learning"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:filtering"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:kernel_methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:machine_learning"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:cesa-bianchi.nicolo"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:low-regret_learning"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1111.6801">
    <title>[1111.6801] The direct L2 geometric structure on a manifold of probability densities with applications to Filtering</title>
    <dc:date>2011-12-01T14:25:45+00:00</dc:date>
    <link>http://arxiv.org/abs/1111.6801</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["In this paper we introduce a projection method for the space of probability distributions based on the differential geometric approach to statistics. This method is based on a direct L2 metric as opposed to the usual Hellinger distance and the related Fisher Information metric. We explain how this apparatus can be used for the nonlinear filtering problem, in relationship also to earlier projection methods based on the Fisher metric. Past projection filters focused on the Fisher metric and the exponential families that made the filter correction step exact. In this work we introduce the mixture projection filter, namely the projection filter based on the direct $L^2$ metric and based on a manifold given by a mixture of pre-assigned densities. The resulting prediction step in the filtering problem is described by a linear differential equation, while the correction step can be made exact."]]></description>
<dc:subject>filtering state_estimation information_geometry time_series in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:bb72e66ca622/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:filtering"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:state_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:information_geometry"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:time_series"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://www.springerlink.com/content/n64824610x241816/">
    <title>Ergodicity of Hidden Markov Model - Mathematics of Control, Signals, and Systems (MCSS), Volume 17, Number 4</title>
    <dc:date>2011-10-28T20:37:18+00:00</dc:date>
    <link>http://www.springerlink.com/content/n64824610x241816/</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["In this paper we study ergodic properties of hidden Markov models with a generalized observation structure. In particular sufficient conditions for the existence of a unique invariant measure for the pair filter-observation are given. Furthermore, necessary and sufficient conditions for the existence of a unique invariant measure of the triple state-observation-filter are provided in terms of asymptotic stability in probability of incorrectly initialized filters. We also study the asymptotic properties of the filter and of the state estimator based on the observations as well as on the knowledge of the initial state. Their connection with minimal and maximal invariant measures is also studied."]]></description>
<dc:subject>in_NB stochastic_processes ergodic_theory markov_models filtering re:almost_none</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:895c1aed90ac/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:ergodic_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:markov_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:filtering"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:almost_none"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1108.3968">
    <title>[1108.3968] Online Expectation Maximization based algorithms for inference in hidden Markov models</title>
    <dc:date>2011-08-22T14:07:33+00:00</dc:date>
    <link>http://arxiv.org/abs/1108.3968</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["The Expectation Maximization (EM) algorithm is a versatile tool for model parameter estimation in latent data models. When processing large data sets or data stream however, EM becomes intractable since it requires the whole data set to be available at each iteration of the algorithm. In this contribution, a new generic online EM algorithm for model parameter inference in general Hidden Markov Model is proposed. This new algorithm updates the parameter estimate after a block of observations is processed (online). The convergence of this new algorithm is established, and the rate of convergence is studied showing the impact of the block size. An averaging procedure is also proposed to improve the rate of convergence. Finally, practical illustrations are presented as well as extensions to some online stochastic EM when Sequential Monte Carlo methods have to be used in combination, in order to make the E-step tractable."
]]></description>
<dc:subject>filtering expectation-maximization markov_models statistics statistical_inference_for_stochastic_processes in_NB</dc:subject>
<dc:identifier>https://pinboard.in/u:cshalizi/b:8b347898d1d4/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:filtering"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:expectation-maximization"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:markov_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistical_inference_for_stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://projecteuclid.org/DPubS?service=UI&amp;version=1.0&amp;verb=Display&amp;handle=euclid.aoap/1287494562">
    <title>Chigansky , van Handel : A complete solution to Blackwell’s unique ergodicity problem for hidden Markov chains</title>
    <dc:date>2010-11-11T12:14:42+00:00</dc:date>
    <link>http://projecteuclid.org/DPubS?service=UI&amp;version=1.0&amp;verb=Display&amp;handle=euclid.aoap/1287494562</link>
    <dc:creator>cshalizi</dc:creator><dc:subject>markov_models in_NB filtering ergodic_theory stochastic_processes heard_the_talk van_handel.ramon</dc:subject>
<dc:identifier>https://pinboard.in/u:cshalizi/b:777150583cb8/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:markov_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:filtering"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:ergodic_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:heard_the_talk"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:van_handel.ramon"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://projecteuclid.org/DPubS?service=UI&amp;version=1.0&amp;verb=Display&amp;handle=euclid.ss/1280841735">
    <title>Carvalho, Johannes, Lopes, Polson: Particle Learning and Smoothing</title>
    <dc:date>2010-08-05T21:35:20+00:00</dc:date>
    <link>http://projecteuclid.org/DPubS?service=UI&amp;version=1.0&amp;verb=Display&amp;handle=euclid.ss/1280841735</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Particle learning (PL) provides state filtering, sequential parameter learning and smoothing in a general class of state space models. Our approach extends existing particle methods by incorporating the estimation of static parameters via a fully-adapted filter that utilizes conditional sufficient statistics for parameters and/or states as particles. State smoothing in the presence of parameter uncertainty is also solved as a by-product of PL. In a number of examples, we show that PL outperforms existing particle filtering alternatives and proves to be a competitor to MCMC."
]]></description>
<dc:subject>particle_filters filtering state-space_models state_estimation estimation time_series statistics</dc:subject>
<dc:identifier>https://pinboard.in/u:cshalizi/b:d276dc573d58/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:particle_filters"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:filtering"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:state-space_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:state_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:time_series"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://pubs.amstat.org/doi/abs/10.1198/jcgs.2010.09051">
    <title>&quot;Fixed Rank Filtering for Spatio-Temporal Data&quot; (Cressie, Shi, Kang)</title>
    <dc:date>2010-08-05T20:59:01+00:00</dc:date>
    <link>http://pubs.amstat.org/doi/abs/10.1198/jcgs.2010.09051</link>
    <dc:creator>cshalizi</dc:creator><dc:subject>filtering spatial_statistics statistics</dc:subject>
<dc:identifier>https://pinboard.in/u:cshalizi/b:e089aaabf6ab/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:filtering"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:spatial_statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://pubs.amstat.org/doi/abs/10.1198/jasa.2009.tm08326">
    <title>Approximate Methods for State-Space Models - Journal of the American Statistical Association - 105(489):170</title>
    <dc:date>2010-03-31T16:58:37+00:00</dc:date>
    <link>http://pubs.amstat.org/doi/abs/10.1198/jasa.2009.tm08326</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA[Huzzah!
]]></description>
<dc:subject>self-centered markov_models state_estimation filtering laplace_approximation stochastic_processes statistical_inference_for_stochastic_processes time_series statistics</dc:subject>
<dc:identifier>https://pinboard.in/u:cshalizi/b:1d0aef660408/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:self-centered"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:markov_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:state_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:filtering"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:laplace_approximation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistical_inference_for_stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:time_series"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://projecteuclid.org/DPubS?service=UI&amp;version=1.0&amp;verb=Display&amp;handle=euclid.imsc/1207580091">
    <title>Bengtsson, Bickel, Li: Curse-of-dimensionality revisited: Collapse of the particle filter in very large scale systems</title>
    <dc:date>2009-12-31T17:43:32+00:00</dc:date>
    <link>http://projecteuclid.org/DPubS?service=UI&amp;version=1.0&amp;verb=Display&amp;handle=euclid.imsc/1207580091</link>
    <dc:creator>cshalizi</dc:creator><dc:subject>filtering state_estimation particle_filters monte_carlo time_series statistics high-dimensional_statistics have_read in_NB re:fitness_sampling</dc:subject>
<dc:identifier>https://pinboard.in/u:cshalizi/b:26e6f5824bf4/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:filtering"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:state_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:particle_filters"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:monte_carlo"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:time_series"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:high-dimensional_statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:have_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:fitness_sampling"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://en.wikipedia.org/wiki/Hodrick-Prescott_filter">
    <title>Hodrick-Prescott filter - Wikipedia, the free encyclopedia</title>
    <dc:date>2009-09-11T16:33:58+00:00</dc:date>
    <link>http://en.wikipedia.org/wiki/Hodrick-Prescott_filter</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA[I think you mis-spelled "smoothing spline".  HTH.  HAND.
]]></description>
<dc:subject>time_series macroeconomics filtering splines wheels:reinvention_of statistics econometrics re:your_favorite_dsge_sucks</dc:subject>
<dc:identifier>https://pinboard.in/u:cshalizi/b:f4d84be694ae/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:time_series"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:macroeconomics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:filtering"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:splines"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:wheels:reinvention_of"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:econometrics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:your_favorite_dsge_sucks"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&amp;id=PLEEE8000079000006066206000001&amp;idtype=cvips&amp;gifs=Yes">
    <title>Failures of sequential Bayesian filters and the successes of shadowing filters in tracking of nonlinear deterministic and stochastic systems</title>
    <dc:date>2009-07-04T19:48:47+00:00</dc:date>
    <link>http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&amp;id=PLEEE8000079000006066206000001&amp;idtype=cvips&amp;gifs=Yes</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Sequential Bayesian filters, such as particle filters, are often presented as an ideal means of tracking the state of nonlinear systems. Here shadowing filters are demonstrated to perform better than sequential filters at tracking under specific circumstances. The success of shadowing filters is attributed to avoiding both well-known deficiencies of particle filters, and some newly identified problems."  Huh.
]]></description>
<dc:subject>particle_filters filtering state_estimation state-space_models time_series</dc:subject>
<dc:identifier>https://pinboard.in/u:cshalizi/b:b31f250173c5/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:particle_filters"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:filtering"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:state_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:state-space_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:time_series"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19860003843_1986003843.pdf">
    <title>Discovery of the Kalman Filter as a Practical Tool for Aerospace and Industry (McGee and Schmidt)</title>
    <dc:date>2009-06-12T23:22:59+00:00</dc:date>
    <link>http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19860003843_1986003843.pdf</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA[So, how _do_ you aim for the stars and/or make sure you hit London?
]]></description>
<dc:subject>filtering state_estimation kalman_filter extended_kalman_filter apollo_project nasa history_of_technology time_series simulation scientific_computing to:blog control_theory_and_control_engineering</dc:subject>
<dc:identifier>https://pinboard.in/u:cshalizi/b:91655a81405f/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:filtering"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:state_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:kalman_filter"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:extended_kalman_filter"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:apollo_project"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:nasa"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:history_of_technology"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:time_series"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:simulation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:scientific_computing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:blog"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:control_theory_and_control_engineering"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://www3.interscience.wiley.com/journal/121581722/abstract">
    <title>Large-scale multiple testing under dependence</title>
    <dc:date>2009-04-07T12:11:42+00:00</dc:date>
    <link>http://www3.interscience.wiley.com/journal/121581722/abstract</link>
    <dc:creator>cshalizi</dc:creator><dc:subject>hypothesis_testing change-point_problem stochastic_processes statistics in_NB have_read filtering markov_models cai.t._tony epidemic_models re:social_networks_as_sensor_networks</dc:subject>
<dc:identifier>https://pinboard.in/u:cshalizi/b:ad34ab6f6d7c/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:hypothesis_testing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:change-point_problem"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:have_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:filtering"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:markov_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:cai.t._tony"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:epidemic_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:social_networks_as_sensor_networks"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://www.springer.com/math/probability/book/978-0-387-76895-3">
    <title>Fundamentals of Stochastic Filtering</title>
    <dc:date>2009-03-20T02:15:42+00:00</dc:date>
    <link>http://www.springer.com/math/probability/book/978-0-387-76895-3</link>
    <dc:creator>cshalizi</dc:creator><dc:subject>books:noted filtering state_estimation stochastic_processes particle_filters books:owned</dc:subject>
<dc:identifier>https://pinboard.in/u:cshalizi/b:a7d625c0adec/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:books:noted"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:filtering"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:state_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:particle_filters"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:books:owned"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://lib.stat.cmu.edu/R/CRAN/web/packages/sspir/index.html">
    <title>CRAN - Package sspir</title>
    <dc:date>2009-02-11T19:41:05+00:00</dc:date>
    <link>http://lib.stat.cmu.edu/R/CRAN/web/packages/sspir/index.html</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA[State-space modeling with linear/Gaussian state evolution and generalized linear models for the observations.  Looks reasonable, lacks a few improvements like diffuse initial conditions in the Kalman filter.
]]></description>
<dc:subject>state-space_models time_series R filtering state_estimation to_teach</dc:subject>
<dc:identifier>https://pinboard.in/u:cshalizi/b:3542f4bd5585/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:state-space_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:time_series"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:R"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:filtering"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:state_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_teach"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://www.ec-securehost.com/SIAM/OT107.html">
    <title>Hidden Markov Models and Dynamical Systems - Andrew Fraser</title>
    <dc:date>2008-11-18T14:26:03+00:00</dc:date>
    <link>http://www.ec-securehost.com/SIAM/OT107.html</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA[Andy's book is appearing in print at last.  (SIAM seems to indicate it's available now, the usual online bookstores say not until the end of the year.)
]]></description>
<dc:subject>markov_models dynamical_systems books:recommended state_estimation filtering state-space_models statistical_inference_for_stochastic_processes via:guslacerda kith_and_kin to_teach:complexity-and-inference fraser.andrew</dc:subject>
<dc:identifier>https://pinboard.in/u:cshalizi/b:c2232e6a78e0/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:markov_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dynamical_systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:books:recommended"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:state_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:filtering"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:state-space_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistical_inference_for_stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:via:guslacerda"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:kith_and_kin"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_teach:complexity-and-inference"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:fraser.andrew"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://www.oup.com/us/catalog/general/subject/Mathematics/AppliedMathematics/?view=usa&amp;ci=9780199219704">
    <title>An Introduction to Stochastic Filtering Theory: Jie Xiong</title>
    <dc:date>2008-05-14T11:30:23+00:00</dc:date>
    <link>http://www.oup.com/us/catalog/general/subject/Mathematics/AppliedMathematics/?view=usa&amp;ci=9780199219704</link>
    <dc:creator>cshalizi</dc:creator><dc:subject>books:noted filtering state_estimation stochastic_processes martingales markov_models branching_processes particle_filters</dc:subject>
<dc:identifier>https://pinboard.in/u:cshalizi/b:521df7b36eee/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:books:noted"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:filtering"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:state_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:martingales"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:markov_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:branching_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:particle_filters"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://www.springerlink.com/content/hk05v4j61686wk27/">
    <title>On error-free filtering of finite-state singular processes under dependent distortions - Prelov and van der Meulen</title>
    <dc:date>2008-02-25T19:29:35+00:00</dc:date>
    <link>http://www.springerlink.com/content/hk05v4j61686wk27/</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA[When can the state of one process be recovered without error from another?  (Use of infinite time limit here is not quite relevant to my immediate needs so must see how to modify proof.)
]]></description>
<dc:subject>filtering state_estimation information_theory re:AoS_project prelov.v._v. van_der_meulen.e._c.</dc:subject>
<dc:identifier>https://pinboard.in/u:cshalizi/b:4b89cf586502/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:filtering"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:state_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:information_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:AoS_project"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:prelov.v._v."/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:van_der_meulen.e._c."/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/0708.3412">
    <title>[0708.3412] Observability and nonlinear filtering</title>
    <dc:date>2007-11-22T04:37:57+00:00</dc:date>
    <link>http://arxiv.org/abs/0708.3412</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["This paper develops a connection between the asymptotic stability of nonlinear filters and a notion of observability. We consider a general class of hidden Markov models in continuous time with compact signal state space, and call such a model observable if no two initial measures of the signal process give rise to the same law of the observation process. We demonstrate that observability implies stability of the filter, i.e., the filtered estimates become insensitive to the initial measure at large times. For the special case where the signal is a finite-state Markov process and the observations are of the white noise type, a complete (necessary and sufficient) characterization of filter stability is obtained in terms of a slightly weaker detectability condition. In addition to observability, the role of controllability in filter stability is explored. Finally, the results are partially extended to non-compact signal state spaces."]]></description>
<dc:subject>markov_models filtering re:AoS_project in_NB van_handel.ramon heard_the_talk</dc:subject>
<dc:identifier>https://pinboard.in/u:cshalizi/b:acac43afaaa3/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:markov_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:filtering"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:AoS_project"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:van_handel.ramon"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:heard_the_talk"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/0710.4245">
    <title>[0710.4245] Particle Filters for Partially Observed Diffusions</title>
    <dc:date>2007-11-09T15:00:08+00:00</dc:date>
    <link>http://arxiv.org/abs/0710.4245</link>
    <dc:creator>cshalizi</dc:creator><dc:subject>particle_filters filtering state-space_models state_estimation stochastic_processes statistics</dc:subject>
<dc:identifier>https://pinboard.in/u:cshalizi/b:a2b3cc7647ef/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:particle_filters"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:filtering"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:state-space_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:state_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
</rdf:Bag></taxo:topics>
</item>
</rdf:RDF>