Transitional Markov Chain Monte Carlo Method For Bayesian Model Updating, Model Class Selection And Model Averaging

• Main Authors: Yi-Ju, Chen, 陳奕竹
• Other Authors: Jian-Ye Ching
• Format: Others
• Language: zh-TW
• Published: 2006
• Online Access: http://ndltd.ncl.edu.tw/handle/4p9f4q

碩士 === 國立臺灣科技大學 === 營建工程系 === 94 === This thesis presents a newly developed stochastic simulation for Bayesian model updating, model class selection and model averaging, named the transitional Markov chain Monte Carlo approach (TMCMC). The idea behind TMCMC is to avoid the problem of sampling from difficult posterior probability density functions (PDF) but sampling from a series of PDFs that converge to the posterior PDF and that are easier to sample. The TMCMC approach is based on Markov chain Monte Carlo (MCMC), while it is more versatile and robust than MCMC. It is shown that TMCMC is able to draw samples from some difficult PDFs, e.g. multi-modal and very peaked PDFs. 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.