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Approximate inference in state space models with intractable likelihoods using Gaussian process optimisation
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.ORCID iD: 0000-0002-9424-1272
Department of Information Technology, Uppsala University.
Linköping University, Department of Computer and Information Science, Statistics. Linköping University, Faculty of Arts and Sciences.
2014 (English)Report (Other academic)
Abstract [en]

We propose a novel method for MAP parameter inference in nonlinear state space models with intractable likelihoods. The method is based on a combination of Gaussian process optimisation (GPO), sequential Monte Carlo (SMC) and approximate Bayesian computations (ABC). SMC and ABC are used to approximate the intractable likelihood by using the similarity between simulated realisations from the model and the data obtained from the system. The GPO algorithm is used for the MAP parameter estimation given noisy estimates of the log-likelihood. The proposed parameter inference method is evaluated in three problems using both synthetic and real-world data. The results are promising, indicating that the proposed algorithm converges fast and with reasonable accuracy compared with existing methods.

Place, publisher, year, edition, pages
2014. , 25 p.
LiTH-ISY-R, ISSN 1400-3902 ; 3075
Keyword [en]
Approximate Bayesian computations, Gaussian process optimisation, Bayesian parameter inference, alpha-stable distribution
National Category
Probability Theory and Statistics Control Engineering Signal Processing
URN: urn:nbn:se:liu:diva-106198ISRN: LiTH-ISY-R-3075OAI: diva2:714542
Swedish Research Council, 621-2013-5524
Available from: 2014-04-28 Created: 2014-04-28 Last updated: 2016-05-04Bibliographically approved
In thesis
1. Sequential Monte Carlo for inference in nonlinear state space models
Open this publication in new window or tab >>Sequential Monte Carlo for inference in nonlinear state space models
2014 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

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.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2014. 118 p.
Linköping Studies in Science and Technology. Thesis, ISSN 0280-7971 ; 1652
National Category
Control Engineering
urn:nbn:se:liu:diva-106752 (URN)10.3384/lic.diva-106752 (DOI)LIU-TEK-LIC-2014:85 (Local ID)978-91-7519-369-4 (print) (ISBN)LIU-TEK-LIC-2014:85 (Archive number)LIU-TEK-LIC-2014:85 (OAI)
2014-05-28, Visionen, B-building, Campus Valla, Linköpings universitet, Linköping, 10:15 (English)
Available from: 2014-05-21 Created: 2014-05-21 Last updated: 2016-05-04Bibliographically approved

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