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

Takashi Kamihigashi and Hiroyuki Watanabe
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Hiroyuki Watanabe: Research Institute for Economics & Business Administration (RIEB), Kobe University, Japan

No DP2016-36, Discussion Paper Series from Research Institute for Economics & Business Administration, Kobe University

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 fiter 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; and (iii) as I increases to 1, 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 only 10. This does not significantly increase computation time if a computer with at least 10 threads is used.

Keywords: Multiple-try method; Particle marginal Metropolis-Hastings; Markov chain Monte Carlo; Mixing; State space models (search for similar items in EconPapers)
Pages: 40 pages
Date: 2016-11
New Economics Papers: this item is included in nep-cmp and nep-ecm
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