liu.seSearch for publications in DiVA
Change search
ReferencesLink to record
Permanent link

Direct link
Hierarchical Bayesian approaches for robust inference in ARX models
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
Dept. of Information Technology, Uppsala University, Uppsala, Sweden.
School of EECS, University of Newcastle, Australia .
2012 (English)In: Proceedings from the 16th IFAC Symposium on System Identification, 2012 / [ed] Michel Kinnaert, 2012, 131-136 p.Conference paper, Presentation (Refereed)
Abstract [en]

Gaussian innovations are the typical choice in most ARX models but using other distributions such as the Student's t could be useful. We demonstrate that this choice of distribution for the innovations provides an increased robustness to data anomalies, such as outliers and missing observations. We consider these models in a Bayesian setting and perform inference using numerical procedures based on Markov Chain Monte Carlo methods. These models include automatic order determination by two alternative methods, based on a parametric model order and a sparseness prior, respectively. The methods and the advantage of our choice of innovations are illustrated in three numerical studies using both simulated data and real EEG data.

Place, publisher, year, edition, pages
2012. 131-136 p.
, IFAC papers online, ISSN 1474-6670 ; 2012
Keyword [en]
Particle Filtering/Monte Carlo Methods; Bayesian Methods
National Category
Signal Processing
URN: urn:nbn:se:liu:diva-81258DOI: 10.3182/20120711-3-BE-2027.00318ISBN: 978-3-902823-06-9OAI: diva2:551244
The 16th IFAC Symposium on System Identification, July 11-13, Brussels, Belgium.
Swedish Research Council
Available from: 2012-09-10 Created: 2012-09-10 Last updated: 2014-05-21Bibliographically 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: 2014-05-27Bibliographically approved

Open Access in DiVA

fulltext(536 kB)348 downloads
File information
File name FULLTEXT01.pdfFile size 536 kBChecksum SHA-512
Type fulltextMimetype application/pdf

Other links

Publisher's full text

Search in DiVA

By author/editor
Dahlin, JohanLindsten, FredrikSchön, Thomas Bo
By organisation
Automatic ControlThe Institute of Technology
Signal Processing

Search outside of DiVA

GoogleGoogle Scholar
Total: 348 downloads
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

Altmetric score

Total: 161 hits
ReferencesLink to record
Permanent link

Direct link