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

Qifan Song; Mingqi Wu; Faming Liang

doi:10.1017/s0001867800007540

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

Qifan Song, Mingqi Wu, Faming Liang

Research output: Contribution to journal › Article › peer-review

15 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 language	English (US)
Pages (from-to)	1059-1083
Number of pages	25
Journal	Advances in Applied Probability
Volume	46
Issue number	4
DOIs	https://doi.org/10.1017/s0001867800007540
State	Published - 2014
Externally published	Yes

ASJC Scopus subject areas

Applied Mathematics
Statistics and Probability

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title = "WEAK CONVERGENCE RATES OF POPULATION VERSUS SINGLE-CHAIN STOCHASTIC APPROXIMATION MCMC ALGORITHMS",

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.",

author = "Qifan Song and Mingqi Wu and Faming Liang",

note = "KAUST Repository Item: Exported on 2021-10-15 Acknowledged 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.",

year = "2014",

doi = "10.1017/s0001867800007540",

language = "English (US)",

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publisher = "Cambridge University Press",

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AU - Song, Qifan

AU - Wu, Mingqi

AU - Liang, Faming

N1 - KAUST Repository Item: Exported on 2021-10-15 Acknowledged 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.

PY - 2014

Y1 - 2014

N2 - 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.

AB - 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.

UR - http://hdl.handle.net/10754/672846

UR - https://www.cambridge.org/core/product/identifier/S0001867800007540/type/journal_article

U2 - 10.1017/s0001867800007540

DO - 10.1017/s0001867800007540

M3 - Article

SN - 1475-6064

VL - 46

SP - 1059

EP - 1083

JO - Advances in Applied Probability

JF - Advances in Applied Probability

IS - 4

ER -

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

Abstract

ASJC Scopus subject areas

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