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 language | English (US) |
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Pages (from-to) | 1059-1083 |
Number of pages | 25 |
Journal | Advances in Applied Probability |
Volume | 46 |
Issue number | 4 |
DOIs | |
State | Published - 2014 |
Externally published | Yes |
Bibliographical note
KAUST Repository Item: Exported on 2021-10-15Acknowledged KAUST grant number(s): KUS-C1-016-04
Acknowledgements: Liang's research was supported in part by the National Science Foundation grants DMS-1106494 and DMS-1317131, and the King Abdullah University of Science and Technology (KAUST) award KUS-C1-016-04. The authors thank the editor, the associate editor, and the anonymous referee for constructive comments that led to a significant improvement of this paper.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.
ASJC Scopus subject areas
- Applied Mathematics
- Statistics and Probability