Sequential Monte Carlo for inference in nonlinear state space models

Nonlinear state space models (SSMs) are a useful class of models to describe many different kinds of systems. Some examples of its applications are to model; the volatility in financial markets, the number of infected persons during an influenza epidemic and the annual number of major earthquakes ar...

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Main Author: Dahlin, Johan
Format: Others
Language:English
Published: Linköpings universitet, Reglerteknik 2014
Online Access:http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-106752
http://nbn-resolving.de/urn:isbn:978-91-7519-369-4 (print)
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spelling ndltd-UPSALLA1-oai-DiVA.org-liu-1067522016-05-05T05:12:21ZSequential Monte Carlo for inference in nonlinear state space modelsengDahlin, JohanLinköpings universitet, ReglerteknikLinköpings universitet, Tekniska högskolanLinköping2014Nonlinear state space models (SSMs) are a useful class of models to describe many different kinds of systems. Some examples of its applications are to model; the volatility in financial markets, the number of infected persons during an influenza epidemic and the annual number of major earthquakes around the world. In this thesis, we are concerned with state inference, parameter inference and input design for nonlinear SSMs based on sequential Monte Carlo (SMC) methods. The state inference problem consists of estimating some latent variable that is not directly observable in the output from the system. The parameter inference problem is concerned with fitting a pre-specified model structure to the observed output from the system. In input design, we are interested in constructing an input to the system, which maximises the information that is available about the parameters in the system output. All of these problems are analytically intractable for nonlinear SSMs. Instead, we make use of SMC to approximate the solution to the state inference problem and to solve the input design problem. Furthermore, we make use of Markov chain Monte Carlo (MCMC) and Bayesian optimisation (BO) to solve the parameter inference problem. In this thesis, we propose new methods for parameter inference in SSMs using both Bayesian and maximum likelihood inference. More specifically, we propose a new proposal for the particle Metropolis-Hastings algorithm, which includes gradient and Hessian information about the target distribution. We demonstrate that the use of this proposal can reduce the length of the burn-in phase and improve the mixing of the Markov chain. Furthermore, we develop a novel parameter inference method based on the combination of BO and SMC. We demonstrate that this method requires a relatively small amount of samples from the analytically intractable likelihood, which are computationally costly to obtain. Therefore, it could be a good alternative to other optimisation based parameter inference methods. The proposed BO and SMC combination is also extended for parameter inference in nonlinear SSMs with intractable likelihoods using approximate Bayesian computations. This method is used for parameter inference in a stochastic volatility model with -stable returns using real-world financial data. Finally, we develop a novel method for input design in nonlinear SSMs which makes use of SMC methods to estimate the expected information matrix. This information is used in combination with graph theory and convex optimisation to estimate optimal inputs with amplitude constraints. We also consider parameter estimation in ARX models with Student-t innovations and unknown model orders. Two different algorithms are used for this inference: reversible Jump Markov chain Monte Carlo and Gibbs sampling with sparseness priors. These methods are used to model real-world EEG data with promising results. Licentiate thesis, comprehensive summaryinfo:eu-repo/semantics/masterThesistexthttp://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-106752urn:isbn:978-91-7519-369-4 (print)doi:10.3384/lic.diva-106752Local LIU-TEK-LIC-2014:85Linköping Studies in Science and Technology. Thesis, 0280-7971 ; 1652application/pdfinfo:eu-repo/semantics/openAccess
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language English
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description Nonlinear state space models (SSMs) are a useful class of models to describe many different kinds of systems. Some examples of its applications are to model; the volatility in financial markets, the number of infected persons during an influenza epidemic and the annual number of major earthquakes around the world. In this thesis, we are concerned with state inference, parameter inference and input design for nonlinear SSMs based on sequential Monte Carlo (SMC) methods. The state inference problem consists of estimating some latent variable that is not directly observable in the output from the system. The parameter inference problem is concerned with fitting a pre-specified model structure to the observed output from the system. In input design, we are interested in constructing an input to the system, which maximises the information that is available about the parameters in the system output. All of these problems are analytically intractable for nonlinear SSMs. Instead, we make use of SMC to approximate the solution to the state inference problem and to solve the input design problem. Furthermore, we make use of Markov chain Monte Carlo (MCMC) and Bayesian optimisation (BO) to solve the parameter inference problem. In this thesis, we propose new methods for parameter inference in SSMs using both Bayesian and maximum likelihood inference. More specifically, we propose a new proposal for the particle Metropolis-Hastings algorithm, which includes gradient and Hessian information about the target distribution. We demonstrate that the use of this proposal can reduce the length of the burn-in phase and improve the mixing of the Markov chain. Furthermore, we develop a novel parameter inference method based on the combination of BO and SMC. We demonstrate that this method requires a relatively small amount of samples from the analytically intractable likelihood, which are computationally costly to obtain. Therefore, it could be a good alternative to other optimisation based parameter inference methods. The proposed BO and SMC combination is also extended for parameter inference in nonlinear SSMs with intractable likelihoods using approximate Bayesian computations. This method is used for parameter inference in a stochastic volatility model with -stable returns using real-world financial data. Finally, we develop a novel method for input design in nonlinear SSMs which makes use of SMC methods to estimate the expected information matrix. This information is used in combination with graph theory and convex optimisation to estimate optimal inputs with amplitude constraints. We also consider parameter estimation in ARX models with Student-t innovations and unknown model orders. Two different algorithms are used for this inference: reversible Jump Markov chain Monte Carlo and Gibbs sampling with sparseness priors. These methods are used to model real-world EEG data with promising results.
author Dahlin, Johan
spellingShingle Dahlin, Johan
Sequential Monte Carlo for inference in nonlinear state space models
author_facet Dahlin, Johan
author_sort Dahlin, Johan
title Sequential Monte Carlo for inference in nonlinear state space models
title_short Sequential Monte Carlo for inference in nonlinear state space models
title_full Sequential Monte Carlo for inference in nonlinear state space models
title_fullStr Sequential Monte Carlo for inference in nonlinear state space models
title_full_unstemmed Sequential Monte Carlo for inference in nonlinear state space models
title_sort sequential monte carlo for inference in nonlinear state space models
publisher Linköpings universitet, Reglerteknik
publishDate 2014
url http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-106752
http://nbn-resolving.de/urn:isbn:978-91-7519-369-4 (print)
work_keys_str_mv AT dahlinjohan sequentialmontecarloforinferenceinnonlinearstatespacemodels
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