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A flexible particle Markov chain Monte Carlo method

  • Eduardo F. Mendes
  • Christopher K. CarterEmail author
  • David Gunawan
  • Robert Kohn
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.

Keywords

Diffusion equation Factor stochastic volatility model Metropolis–Hastings Particle Gibbs sampler 

Notes

Acknowledgements

The work of the authors was partially supported by an ARC Research Council Grant DP120104014. The work of Robert Kohn and David Gunawan was also partially supported by the ARC Center of Excellence Grant CE140100049.

Supplementary material

11222_2019_9916_MOESM1_ESM.pdf (494 kb)
Supplementary material 1 (pdf 494 KB)

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2020

Authors and Affiliations

  1. 1.School of Applied MathematicsFundação Getulio VargasRio de JaneiroBrazil
  2. 2.School of EconomicsUniversity of New South WalesSydneyAustralia

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