Title

A Multiple-Try Extension of the Particle Marginal Metropolis-Hastings (PMMH) Algorithm with an Independent Proposal

Abstract

In this paper we propose a multiple-try extension of the PMMH algorithm with an independent proposal. In our algorithm, I ∈ ℕ parameter particles are sampled from the independent proposal. For each of them, a particle filter with K ∈ ℕ state particles is run. We show that the algorithm has the following properties: (i) the distribution of the Markov chain generated by the algorithm converges to the posterior of interest in total variation; (ii) as I increases to ∞, the acceptance probability at each iteration converges to 1 with probability 1; and (iii) as I increases to ∞, the autocorrelation of any order for any parameter with bounded support converges to 0. These results indicate that the algorithm generates almost i.i.d. samples from the posterior for sufficiently large I. Our numerical experiments suggest that one can visibly improve mixing by increasing I from 1 to a small number. This does not significantly increase computation time if a computer with at least the same number of threads is used.

Keywords

Multiple-try method, Particle marginal Metropolis-Hastings, Markov chain Monte Carlo, Mixing, State space models


Inquiries

Takashi KAMIHIGASHI
Research Institute for Economics and Business Administration,
Kobe University
Rokkodai-cho, Nada-ku, Kobe
657-8501 Japan
Phone: +81-78-803-7036
FAX: +81-78-803-7059

Hiroyuki WATANABE
Research Institute for Economics and Business Administration,
Kobe University
Rokkodai-cho, Nada-ku, Kobe
657-8501 Japan
Phone: +81-78-803-7036
FAX: +81-78-803-7059