A flexible particle Markov chain Monte Carlo method

Particle Markov Chain Monte Carlo methods are used to carry out inference in nonlinear and non-Gaussian state space models, where the posterior density of the states is approximated using particles. Current approaches usually perform Bayesian inference using either a particle marginal Metropolis–Has...

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Bibliographic Details
Published inStatistics and computing Vol. 30; no. 4; pp. 783 - 798
Main Authors Mendes, Eduardo F., Carter, Christopher K., Gunawan, David, Kohn, Robert
Format Journal Article
LanguageEnglish
Published New York Springer US 01.07.2020
Springer Nature B.V
Subjects
Algorithms
Artificial Intelligence
Bayesian analysis
Computer simulation
Convergence
Markov analysis
Markov chains
Mathematics and Statistics
Monte Carlo simulation
Parameters
Probability and Statistics in Computer Science
Sampling
State space models
Statistical inference
Statistical Theory and Methods
Statistics
Statistics and Computing/Statistics Programs
Stochastic models
Volatility
Particle Gibbs sampler
Metropolis–Hastings
Diffusion equation
Factor stochastic volatility model
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Summary:Particle Markov Chain Monte Carlo methods are used to carry out inference in nonlinear and non-Gaussian state space models, where the posterior density of the states is approximated using particles. Current approaches usually perform Bayesian inference using either a particle marginal Metropolis–Hastings (PMMH) algorithm or a particle Gibbs (PG) sampler. This paper shows how the two ways of generating variables mentioned above can be combined in a flexible manner to give sampling schemes that converge to a desired target distribution. The advantage of our approach is that the sampling scheme can be tailored to obtain good results for different applications. For example, when some parameters and the states are highly correlated, such parameters can be generated using PMMH, while all other parameters are generated using PG because it is easier to obtain good proposals for the parameters within the PG framework. We derive some convergence properties of our sampling scheme and also investigate its performance empirically by applying it to univariate and multivariate stochastic volatility models and comparing it to other PMCMC methods proposed in the literature.
ISSN:0960-3174
1573-1375
DOI:10.1007/s11222-019-09916-7