Weak Convergence Rates of Population versus Single-Chain Stochastic Approximation MCMC Algorithms
Statistics Theory
2013-10-29 v1 Statistics Theory
Abstract
In this paper, we establish the theory of weak convergence (toward a normal distribution) for both single-chain and population stochastic approximation MCMC 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.
Cite
@article{arxiv.1310.7479,
title = {Weak Convergence Rates of Population versus Single-Chain Stochastic Approximation MCMC Algorithms},
author = {Qifan Song and Mingqi Wu and Faming Liang},
journal= {arXiv preprint arXiv:1310.7479},
year = {2013}
}
Comments
36 pages