Biased Online Parameter Inference for State-Space Models

Moral, Pierre Del; Jasra, Ajay; Zhou, Yan

doi:10.1007/s11009-016-9511-x

Cited by 7 publications

(9 citation statements)

References 20 publications

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“…In order to illustrate the theoretical results, we present computer simulations for a stochastic Lorenz 63 model which show, numerically, how the nested particle filtering algorithm attains an accurate and stable performance with a fixed number of particles and long sequences of observations. A brief comparison with the truncated SMC 2 method of [14] is also included.…”

Section: Contributionsmentioning

confidence: 99%

“…using Markov chain Monte Carlo (MCMC) kernels. A natural example is the algorithm of [14], which relies on a particle MCMC [1] kernel to update the random grid {θ…”

Section: Sampling In the Parameter Spacementioning

confidence: 99%

“…where c < ∞ is independent of N . To find a convergence rate for the second term in (14), we expand the conditional expectations to obtain…”

Section: Uniform Convergence Of the Inner Particle Filtersmentioning

confidence: 99%

“…We have also run, for comparison, the truncated SMC 2 algorithm of [14] with a window size of 40 observations and resampling steps when the effective sample size of the particles in the parameter space goes below N/3. The sampling step of this method is implemented using a particle Metropolis-Hastings [1] procedure.…”

Section: Theorem 2 Let D θ Be a Compact Set And κ Nρ A Kernel Of Thmentioning

confidence: 99%

“…The recent sequential Monte Carlo square (SMC 2 ) method [7] overcomes these problems, but the algorithm is not recursive and, hence, it becomes computationally prohibitive when the sequence of observations is relatively long. A version of the SMC 2 method in which the observations are processed in blocks of fixed size has been proposed in [14]. This scheme is recursive and bears similarity to the method we analyse in this paper.…”

Section: Introductionmentioning

confidence: 99%

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Uniform convergence over time of a nested particle filtering scheme for recursive parameter estimation in state-space Markov models

Crisan

Mı́guez

2017

Adv. Appl. Probab.

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We analyse the performance of a recursive Monte Carlo method for the Bayesian estimation of the static parameters of a discrete-time state-space Markov model. The algorithm employs two layers of particle filters to approximate the posterior probability distribution of the model parameters. In particular, the first layer yields an empirical distribution of samples on the parameter space, while the filters in the second layer are auxiliary devices to approximate the (analytically intractable) likelihood of the parameters. This approach relates the this algorithm to the recent sequential Monte Carlo square (SMC 2 ) method, which provides a non-recursive solution to the same problem. In this paper, we investigate the approximation, via the proposed scheme, of integrals of real bounded functions with respect to the posterior distribution of the system parameters. Under assumptions related to the compactness of the parameter support and the stability and continuity of the sequence of posterior distributions for the state-space model, we prove that the L p norms of the approximation errors vanish asymptotically (as the number of Monte Carlo samples generated by the algorithm increases) and uniformly over time. We also prove that, under the same assumptions, the proposed scheme can asymptotically identify the parameter values for a class of models. We conclude the paper with a numerical example that illustrates the uniform convergence results by exploring the accuracy and stability of the proposed algorithm operating with long sequences of observations.

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Section: Contributionsmentioning

confidence: 99%

“…using Markov chain Monte Carlo (MCMC) kernels. A natural example is the algorithm of [14], which relies on a particle MCMC [1] kernel to update the random grid {θ…”

Section: Sampling In the Parameter Spacementioning

confidence: 99%

“…where c < ∞ is independent of N . To find a convergence rate for the second term in (14), we expand the conditional expectations to obtain…”

Section: Uniform Convergence Of the Inner Particle Filtersmentioning

confidence: 99%

Section: Theorem 2 Let D θ Be a Compact Set And κ Nρ A Kernel Of Thmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Uniform convergence over time of a nested particle filtering scheme for recursive parameter estimation in state-space Markov models

Crisan

Mı́guez

2017

Adv. Appl. Probab.

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Sequential Bayesian inference for spatio-temporal models of temperature and humidity data

Lai

Golightly

Boys

2020

Journal of Computational Science

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Sequential Bayesian inference for implicit hidden Markov models and current limitations

Jacob

2015

ESAIM: Proc.

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Abstract. Hidden Markov models can describe time series arising in various fields of science, by treating the data as noisy measurements of an arbitrarily complex Markov process. Sequential Monte Carlo (SMC) methods have become standard tools to estimate the hidden Markov process given the observations and a fixed parameter value. We review some of the recent developments allowing the inclusion of parameter uncertainty as well as model uncertainty. The shortcomings of the currently available methodology are emphasised from an algorithmic complexity perspective. The statistical objects of interest for time series analysis are illustrated on a toy "Lotka-Volterra" model used in population ecology. Some open challenges are discussed regarding the scalability of the reviewed methodology to longer time series, higher-dimensional state spaces and more flexible models.Résumé. Les modèlesà chaîne de Markov cachée permettent de décrire les séries temporelles de divers domaines scientifiques, en traitant les données comme des mesures bruitées d'un processus de Markov arbitrairement complexe. Les méthodes de Monte Carlo séquentielles (SMC) sont devenues des outils standards pour l'estimation du processus de Markov caché sachant les observations et une valeur fixée du paramètre. Nous passons en revue quelques unes des récentes avancées permettant de prendre en compte l'incertitude sur le paramètre ainsi que l'incertitude sur le modèle. Les limites de la méthodologie actuelle sont discutées sous l'angle de la complexité algorithmique. Les objets statistiques d'intérêt pour l'analyse des séries temporelles sont illustrés sur un modèle jouet de type "Lotka-Volterra" utilisé enécologie des populations. Quelques questions ouvertes sont finalement posées concernant l'extension de la méthodologie présentée pour traiter des séries de données plus longues, des espaces d'états de dimension plus grande et des modèles plus flexibles.

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Biased Online Parameter Inference for State-Space Models

Cited by 7 publications

References 20 publications

Uniform convergence over time of a nested particle filtering scheme for recursive parameter estimation in state-space Markov models

Uniform convergence over time of a nested particle filtering scheme for recursive parameter estimation in state-space Markov models

Sequential Bayesian inference for spatio-temporal models of temperature and humidity data

Sequential Bayesian inference for implicit hidden Markov models and current limitations

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