Advances in Applied Probability

Weak convergence rates of population versus single-chain stochastic approximation MCMC algorithms

Qifan Song, Mingqi Wu, and Faming Liang

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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.

Article information

Adv. in Appl. Probab., Volume 46, Number 4 (2014), 1059-1083.

First available in Project Euclid: 12 December 2014

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60J22: Computational methods in Markov chains [See also 65C40]
Secondary: 65C05: Monte Carlo methods

Asymptotic normality Markov chain Monte Carlo stochastic approximation Metropolis-Hastings algorithm


Song, Qifan; Wu, Mingqi; Liang, Faming. Weak convergence rates of population versus single-chain stochastic approximation MCMC algorithms. Adv. in Appl. Probab. 46 (2014), no. 4, 1059--1083. doi:10.1239/aap/1418396243.

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