## Population Stochastic Approximation MCMC Algorithm and its Weak Convergence (2010)

### BibTeX

@MISC{Liang10populationstochastic,

author = {Faming Liang and Mingqi Wu},

title = {Population Stochastic Approximation MCMC Algorithm and its Weak Convergence},

year = {2010}

}

### OpenURL

### Abstract

In this paper, we propose a population stochastic approximation MCMC (SAMCMC) algorithm, and establish its weak convergence (toward a normal distribution) under mild conditions. The theory of weak convergence established for the population SAMCMC algorithm is also applicable for general single chain SAMCMC algorithms. Based on the theory, we then give an explicit ratio for the convergence rates of the population SAMCMC algorithm and the single chain SAM-CMC algorithm. The theoretical results are illustrated by a population stochastic approximation Monte Carlo (SAMC) algorithm with a multimodal example. Our results, in both theory and numerical examples, suggest that the population SAMCMC algorithm can be more efficient than the single chain SAMCMC algorithm. This is of interest for practical applications.