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Approximate Bayesian Computation by Subset Simulation

Chiachio, Manuel and Beck, James L. and Chiachio, Juan and Rus, Guillermo (2014) Approximate Bayesian Computation by Subset Simulation. SIAM Journal on Scientific Computing, 36 (3). A1339-A1358. ISSN 1064-8275. http://resolver.caltech.edu/CaltechAUTHORS:20140808-102506649

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Abstract

A new approximate Bayesian computation (ABC) algorithm for Bayesian updating of model parameters is proposed in this paper, which combines the ABC principles with the technique of subset simulation for efficient rare-event simulation, first developed in S. K. Au and J. L. Beck [Probabilistic Engrg. Mech., 16 (2001), pp. 263-277]. It has been named ABC-SubSim. The idea is to choose the nested decreasing sequence of regions in subset simulation as the regions that correspond to increasingly closer approximations of the actual data vector in observation space. The efficiency of the algorithm is demonstrated in two examples that illustrate some of the challenges faced in real-world applications of ABC. We show that the proposed algorithm outperforms other recent sequential ABC algorithms in terms of computational efficiency while achieving the same, or better, measure of accuracy in the posterior distribution. We also show that ABC-SubSim readily provides an estimate of the evidence (marginal likelihood) for posterior model class assessment, as a by-product.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://epubs.siam.org/doi/abs/10.1137/130932831PublisherArticle
http://dx.doi.org/10.1137/130932831DOIArticle
http://arxiv.org/abs/1404.6225arXivArticle
Additional Information:© 2014, Society for Industrial and Applied Mathematics. Submitted to the journal’s Methods and Algorithms for Scientific Computing section August 13, 2013; accepted for publication (in revised form) April 8, 2014; published electronically June 26, 2014. This work was supported by the Spanish Ministry of Economy for project DPI2010-17065 and the European Union for the “Programa Operativo FEDER de Andalucía 2007-2013” for project GGI3000IDIB. The first two authors would like to thank the California Institute of Technology (Caltech) which kindly hosted them during the course of this work.
Funders:
Funding AgencyGrant Number
Spanish Ministry of EconomyDPI2010-17065
European Union for the “Programa Operativo FEDER de Andalucía 2007-2013GGI3000IDIB
Subject Keywords:approximate Bayesian computation, subset simulation, Bayesian inverse problem
Classification Code:AMS: 65D05, 41A63, 41A10
Record Number:CaltechAUTHORS:20140808-102506649
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20140808-102506649
Official Citation:Approximate Bayesian Computation by Subset Simulation Manuel Chiachio, James L. Beck, Juan Chiachio, and Guillermo Rus SIAM Journal on Scientific Computing 2014 36:3, A1339-A1358
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:48239
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:08 Aug 2014 20:22
Last Modified:08 Aug 2014 20:22

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