WEAK CONVERGENCE RATES OF POPULATION VERSUS SINGLE-CHAIN STOCHASTIC APPROXIMATION MCMC ALGORITHMS

Qifan Song, Mingqi Wu, Faming Liang

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

Abstract

In this paper we establish the theory of weak convergence (toward a normal distribution) for both single-chain and population stochastic approximation Markov chain Monte Carlo (MCMC) algorithms (SAMCMC algorithms). Based on the theory, we give an explicit ratio of convergence rates for the population SAMCMC algorithm and the single-chain SAMCMC algorithm. Our results provide a theoretic guarantee that the population SAMCMC algorithms are asymptotically more efficient than the single-chain SAMCMC algorithms when the gain factor sequence decreases slower than O(1 / t), where t indexes the number of iterations. This is of interest for practical applications.
Original languageEnglish (US)
Pages (from-to)1059-1083
Number of pages25
JournalAdvances in Applied Probability
Volume46
Issue number4
DOIs
StatePublished - 2014
Externally publishedYes

ASJC Scopus subject areas

  • Applied Mathematics
  • Statistics and Probability

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