Use of SAMC for Bayesian analysis of statistical models with intractable normalizing constants

Handle URI:
http://hdl.handle.net/10754/600146
Title:
Use of SAMC for Bayesian analysis of statistical models with intractable normalizing constants
Authors:
Jin, Ick Hoon; Liang, Faming
Abstract:
Statistical inference for the models with intractable normalizing constants has attracted much attention. During the past two decades, various approximation- or simulation-based methods have been proposed for the problem, such as the Monte Carlo maximum likelihood method and the auxiliary variable Markov chain Monte Carlo methods. The Bayesian stochastic approximation Monte Carlo algorithm specifically addresses this problem: It works by sampling from a sequence of approximate distributions with their average converging to the target posterior distribution, where the approximate distributions can be achieved using the stochastic approximation Monte Carlo algorithm. A strong law of large numbers is established for the Bayesian stochastic approximation Monte Carlo estimator under mild conditions. Compared to the Monte Carlo maximum likelihood method, the Bayesian stochastic approximation Monte Carlo algorithm is more robust to the initial guess of model parameters. Compared to the auxiliary variable MCMC methods, the Bayesian stochastic approximation Monte Carlo algorithm avoids the requirement for perfect samples, and thus can be applied to many models for which perfect sampling is not available or very expensive. The Bayesian stochastic approximation Monte Carlo algorithm also provides a general framework for approximate Bayesian analysis. © 2012 Elsevier B.V. All rights reserved.
Citation:
Jin IH, Liang F (2014) Use of SAMC for Bayesian analysis of statistical models with intractable normalizing constants. Computational Statistics & Data Analysis 71: 402–416. Available: http://dx.doi.org/10.1016/j.csda.2012.07.005.
Publisher:
Elsevier BV
Journal:
Computational Statistics & Data Analysis
KAUST Grant Number:
KUS-C1-016-04
Issue Date:
Mar-2014
DOI:
10.1016/j.csda.2012.07.005
Type:
Article
ISSN:
0167-9473
Sponsors:
The authors thank the Editor, Associate Editors, and Referees for their comments which have led to significant improvement of this paper. Liang's research was partially supported by grants from the National Science Foundation (DMS-1007457 and CMMI-0926803) and the award (KUS-C1-016-04) made by King Abdullah University of Science and Technology (KAUST).
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Full metadata record

DC FieldValue Language
dc.contributor.authorJin, Ick Hoonen
dc.contributor.authorLiang, Famingen
dc.date.accessioned2016-02-28T06:43:41Zen
dc.date.available2016-02-28T06:43:41Zen
dc.date.issued2014-03en
dc.identifier.citationJin IH, Liang F (2014) Use of SAMC for Bayesian analysis of statistical models with intractable normalizing constants. Computational Statistics & Data Analysis 71: 402–416. Available: http://dx.doi.org/10.1016/j.csda.2012.07.005.en
dc.identifier.issn0167-9473en
dc.identifier.doi10.1016/j.csda.2012.07.005en
dc.identifier.urihttp://hdl.handle.net/10754/600146en
dc.description.abstractStatistical inference for the models with intractable normalizing constants has attracted much attention. During the past two decades, various approximation- or simulation-based methods have been proposed for the problem, such as the Monte Carlo maximum likelihood method and the auxiliary variable Markov chain Monte Carlo methods. The Bayesian stochastic approximation Monte Carlo algorithm specifically addresses this problem: It works by sampling from a sequence of approximate distributions with their average converging to the target posterior distribution, where the approximate distributions can be achieved using the stochastic approximation Monte Carlo algorithm. A strong law of large numbers is established for the Bayesian stochastic approximation Monte Carlo estimator under mild conditions. Compared to the Monte Carlo maximum likelihood method, the Bayesian stochastic approximation Monte Carlo algorithm is more robust to the initial guess of model parameters. Compared to the auxiliary variable MCMC methods, the Bayesian stochastic approximation Monte Carlo algorithm avoids the requirement for perfect samples, and thus can be applied to many models for which perfect sampling is not available or very expensive. The Bayesian stochastic approximation Monte Carlo algorithm also provides a general framework for approximate Bayesian analysis. © 2012 Elsevier B.V. All rights reserved.en
dc.description.sponsorshipThe authors thank the Editor, Associate Editors, and Referees for their comments which have led to significant improvement of this paper. Liang's research was partially supported by grants from the National Science Foundation (DMS-1007457 and CMMI-0926803) and the award (KUS-C1-016-04) made by King Abdullah University of Science and Technology (KAUST).en
dc.publisherElsevier BVen
dc.subjectBayesian analysisen
dc.subjectIntractable normalizing constanten
dc.subjectMarkov chain Monte Carloen
dc.subjectStochastic approximationen
dc.titleUse of SAMC for Bayesian analysis of statistical models with intractable normalizing constantsen
dc.typeArticleen
dc.identifier.journalComputational Statistics & Data Analysisen
dc.contributor.institutionUniversity of Texas M. D. Anderson Cancer Center, Houston, United Statesen
dc.contributor.institutionTexas A and M University, College Station, United Statesen
kaust.grant.numberKUS-C1-016-04en
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