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A flexible particle Markov chain Monte Carlo method

Journal Article


Abstract


  • 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.

Publication Date


  • 2020

Citation


  • Mendes, E. F., Carter, C. K., Gunawan, D., & Kohn, R. (2020). A flexible particle Markov chain Monte Carlo method. Statistics and Computing, 30(4), 783-798. doi:10.1007/s11222-019-09916-7

Scopus Eid


  • 2-s2.0-85078608231

Start Page


  • 783

End Page


  • 798

Volume


  • 30

Issue


  • 4

Abstract


  • 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.

Publication Date


  • 2020

Citation


  • Mendes, E. F., Carter, C. K., Gunawan, D., & Kohn, R. (2020). A flexible particle Markov chain Monte Carlo method. Statistics and Computing, 30(4), 783-798. doi:10.1007/s11222-019-09916-7

Scopus Eid


  • 2-s2.0-85078608231

Start Page


  • 783

End Page


  • 798

Volume


  • 30

Issue


  • 4