Transitional Markov Chain Monte Carlo Method for Bayesian Model Updating, Model Class Selection, and Model Averaging

• Published in: Journal of engineering mechanics Vol. 133; no. 7; pp. 816 - 832
• Main Authors: Ching, Jianye, Chen, Yi-Chu
• Format: Journal Article
• Language: English
• Published: Reston, VA American Society of Civil Engineers 01.07.2007
• Subjects: Exact sciences and technology; Fundamental areas of phenomenology (including applications); Measurement and testing methods; Physics; Solid mechanics; Structural and continuum mechanics; TECHNICAL PAPERS; Bayes estimation; Monte Carlo method; Averaging method; Probabilistic approach; Markov chains; Multimode waveguide; Modeling; Adaptive method; Markov chain; Model matching; Simulation; Probability density function; System identification; Bayesian analysis
• ISSN: 0733-9399; 1943-7889
• DOI: 10.1061/(ASCE)0733-9399(2007)133:7(816)

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.