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Bayesian Theory and Applications$
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Paul Damien, Petros Dellaportas, Nicholas G. Polson, and David A. Stephens

Print publication date: 2013

Print ISBN-13: 9780199695607

Published to Oxford Scholarship Online: May 2013

DOI: 10.1093/acprof:oso/9780199695607.001.0001

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PRINTED FROM OXFORD SCHOLARSHIP ONLINE (www.oxfordscholarship.com). (c) Copyright Oxford University Press, 2019. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use. date: 15 October 2019

Online Bayesian learning in dynamic models: an illustrative introduction to particle methods

Online Bayesian learning in dynamic models: an illustrative introduction to particle methods

Chapter:
(p.203) 11 Online Bayesian learning in dynamic models: an illustrative introduction to particle methods
Source:
Bayesian Theory and Applications
Author(s):

Hedibert F Lopes

Carlos M Carvalho

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199695607.003.0011

This chapter provides a step-by-step review of Monte Carlo (MC) methods for filtering in general nonlinear and non-Gaussian dynamic models, also known as state-space models or hidden Markov models. The chapter is organized as follows. Section 11.2 introduces the basic notation, results, and references for the general class of Gaussian dynamic linear models (DLM), the AR(1) plus noise model, and the standard stochastic volatility model with AR(1) dynamics. Sections 11.3 and 11.4 discuss particle filters for state learning with fixed parameters (also known as pure filtering) and particle filters for state and parameter learning, respectively. Section 11.5 deals with general issues, such as MC error, sequential model checking, particle smoothing, and the interaction between particle filters and Markov chain Monte Carlo (MCMC) schemes.

Keywords:   Monte Carlo methods, filtering, state-space models, hidden Markov modes, Gaussian dynamic linear models, state learning, particle filters, parameter learning, Markov chain Monte Carlo, AR(1) plus noise model

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