Sequential Monte Carlo Methods

Authored by: Marloes Maathuis , Mathias Drton , Steffen Lauritzen , Martin Wainwright

Handbook of Graphical Models

Print publication date:  November  2018
Online publication date:  November  2018

Print ISBN: 9781498788625
eBook ISBN: 9780429463976
Adobe ISBN:

10.1201/9780429463976-7

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Abstract

Inference in probabilistic graphical models is generally analytically intractable for non-Gaussian, continuous-valued models and too computationally expensive for high-dimensional discrete-valued models. In these scenarios, a popular approach to carry out approximate inference consists of using Monte Carlo techniques, as discussed in Section 5.3.5 of Chapter 5. We focus here on Sequential Monte Carlo (SMC) and some related Markov chain Monte Carlo (MCMC) methods. The chapter is structured with a particular application as its main motivating example: inference in the context of discrete state-space hidden Markov models (HMMs). SMC methods are applicable much more generally, for example to general state-space HMMs and to fairly arbitrary models as outlined in Section 1.7. We have chosen to focus on discrete state-space HMMs to emphasize the important ideas: SMC methods for general state-space HMMs are essentially similar but involve notational complications that we would prefer to avoid.

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