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Asymptotically Independent Markov Sampling: A New Markov Chain Monte Carlo Scheme for Bayesian Interference

Beck, James L. and Zuev, Konstantin M. (2013) Asymptotically Independent Markov Sampling: A New Markov Chain Monte Carlo Scheme for Bayesian Interference. International Journal for Uncertainty Quantification, 3 (5). pp. 445-474. ISSN 2152-5099. doi:10.1615/Int.J.UncertaintyQuantification.2012004713. https://resolver.caltech.edu/CaltechAUTHORS:20120817-150031159

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Abstract

In Bayesian statistics, many problems can be expressed as the evaluation of the expectation of a quantity of interest with respect to the posterior distribution. Standard Monte Carlo method is often not applicable because the encountered posterior distributions cannot be sampled directly. In this case, the most popular strategies are the importance sampling method, Markov chain Monte Carlo, and annealing. In this paper, we introduce a new scheme for Bayesian inference, called Asymptotically Independent Markov Sampling (AIMS), which is based on the above methods. We derive important ergodic properties of AIMS. In particular, it is shown that, under certain conditions, the AIMS algorithm produces a uniformly ergodic Markov chain. The choice of the free parameters of the algorithm is discussed and recommendations are provided for this choice, both theoretically and heuristically based. The efficiency of AIMS is demonstrated with three numerical examples, which include both multimodal and higher-dimensional target posterior distributions.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1615/Int.J.UncertaintyQuantification.2012004713DOIUNSPECIFIED
http://arxiv.org/abs/1110.1880arXivUNSPECIFIED
http://www.dl.begellhouse.com/journals/52034eb04b657aea,2cb8d8b565b6c7f1,5fda50933d5a6c1a.htmlPublisherUNSPECIFIED
Additional Information:© 2013 by Begell House, Inc. This work was supported by the National Science Foundation under award number EAR- 0941374 to the California Institute of Technology. This support is gratefully acknowledged. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect those of the National Science Foundation.
Funders:
Funding AgencyGrant Number
NSFEAR-0941374
Subject Keywords:Bayesian inference, uncertainty quantification, Markov chain Monte Carlo, importance sampling, simulated annealing
Issue or Number:5
DOI:10.1615/Int.J.UncertaintyQuantification.2012004713
Record Number:CaltechAUTHORS:20120817-150031159
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20120817-150031159
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:33311
Collection:CaltechAUTHORS
Deposited By: Carmen Nemer-Sirois
Deposited On:21 Aug 2012 23:19
Last Modified:09 Nov 2021 21:33

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