Transitional Markov Chain Monte Carlo Method for Bayesian Model Updating, Model Class Selection, and Model Averaging
Publication: Journal of Engineering Mechanics
Volume 133, Issue 7
Abstract
This paper presents a newly developed simulation-based approach for Bayesian model updating, model class selection, and model averaging called the transitional Markov chain Monte Carlo (TMCMC) approach. The idea behind TMCMC is to avoid the problem of sampling from difficult target probability density functions (PDFs) but sampling from a series of intermediate PDFs that converge to the target PDF and are easier to sample. The TMCMC approach is motivated by the adaptive Metropolis–Hastings method developed by Beck and Au in 2002 and is based on Markov chain Monte Carlo. It is shown that TMCMC is able to draw samples from some difficult PDFs (e.g., multimodal PDFs, very peaked PDFs, and PDFs with flat manifold). The TMCMC approach can also estimate evidence of the chosen probabilistic model class conditioning on the measured data, a key component for Bayesian model class selection and model averaging. Three examples are used to demonstrate the effectiveness of the TMCMC approach in Bayesian model updating, model class selection, and model averaging.
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Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 133 • Issue 7 • July 2007
Pages: 816 - 832
Copyright
© 2007 ASCE.
History
Received: Aug 10, 2005
Accepted: Dec 14, 2006
Published online: Jul 1, 2007
Published in print: Jul 2007
Notes
Note. Associate Editor: Arvid Naess
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