Journal Article

Particle Markov chain Monte Carlo methods

Doucet, Arnaud, Holenstein, Roman, Andrieu, Christophe

2010

Overview

Markov chain Monte Carlo and sequential Monte Carlo methods have emerged as the two main tools to sample from high dimensional probability distributions. Although asymptotic convergence of Markov chain Monte Carlo algorithms is ensured under weak assumptions, the performance of these algorithms is unreliable when the proposal distributions that are used to explore the space are poorly chosen and/or if highly correlated variables are updated independently. We show here how it is possible to build efficient high dimensional proposal distributions by using sequential Monte Carlo methods. This allows us not only to improve over standard Markov chain Monte Carlo schemes but also to make Bayesian inference feasible for a large class of statistical models where this was not previously so. We demonstrate these algorithms on a non-linear state space model and a Lévy-driven stochastic volatility model.

• Publisher: Oxford, UK : Blackwell Publishing Ltd,Blackwell Publishing Ltd,Wiley-Blackwell,Royal Statistical Society,Oxford University Press
• Subject: Algorithms / Approximation / Bayesian analysis / Bayesian inference / Bayesian method / Bayesian theory / Computer simulation / Construction / Convergence / Distribution / Function words / Inference / Markov analysis / Markov chain / Markov chain Monte Carlo methods / Markov chains / Markovian processes / Mathematical models / Methodology / Metropolitan areas / Modeling / Monte Carlo method / Monte Carlo methods / Monte Carlo simulation / Parametric models / Probability / probability distribution / Proposals / Quantum statistics / Railroad transportation / Sampling / Sampling distributions / Sequential Monte Carlo methods / State space models / Statistical analysis / Statistical methods / statistical models / Statistics / Studies / Variables