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research-article

Bayesian Annealed Sequential Importance Sampling (BASIS): an unbiased version of Transitional Markov Chain Monte Carlo

[+] Author and Article Information
Stephen Wu

Postdoctoral, CSELab, ETH-Zurich, CH -8092, Switzerland
stewu@ism.ac.jp

Panagiotis Angelikopoulos

Postdoctoral, CSELab, ETH-Zurich, CH -8092, Switzerland
pangelikopoulos@gmail.com

Costas Papadimitriou

Professor, Department of Mechanical Engineering, University of Thessaly, 38334 Volos, Greece
costasp@mie.uth.gr

Petros Koumoutsakos

Professor, CSELab, ETH-Zurich, CH -8092. Switzerland, Radcliffe Institute of Advanced Study, Harvard University, Cambridge, MA 02138; Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02138
petros@ethz.ch

1Corresponding author.

ASME doi:10.1115/1.4037450 History: Received July 07, 2016; Revised March 27, 2017

Abstract

The Transitional Markov Chain Monte Carlo (TMCMC) is one of the most potent algorithms for performing MCMC in the context of Bayesian uncertainty quantification in parallel computing architectures. However, the features that are associated with its efficient sampling are also responsible for its introducing of a bias in the sampling. We demonstrate that the Markov chains of each subsample in TMCMC may result in uneven chain lengths that distort the intermediate target distribution and introduces bias accumulation in each stage of the TMCMC algorithm. We remedy this drawback of TMCMC by proposing uniform chain lengths, with or without burn-in, so that the algorithm emphasizes Sequential Importance Sampling over MCMC. The proposed Bayesian Annealed Sequential Importance Sampling (BASIS) removes the bias of the original TMCMC and at the same time increases its parallel efficiency. We demonstrate the advantages and drawbacks of BASIS in modeling of bridge dynamics using finite elements and a disk-wall collision using discrete element methods.

Copyright (c) 2017 by ASME
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