Application of the transitional Markov chain Monte Carlo algorithm to probabilistic site characterization

• Published in: Engineering geology 2016-03, Vol.203, p.151-167
• Main Authors: Ching, Jianye, Wang, Jiun-Shiang
• Format: Article
• Language: English
• Subjects: Algorithms; Bayesian methods; Markov chain Monte Carlo; Markov chains; Mathematical models; Monte Carlo methods; Probabilistic methods; Probability density functions; Probability theory; Proposals; Site investigation; Spatial variability; Statistical uncertainty
• ISSN: 0013-7952; 1872-6917
• DOI: 10.1016/j.enggeo.2015.10.015

This paper applies the transitional Markov chain Monte Carlo (TMCMC) algorithm to probabilistic site characterization problems. The purpose is to characterize the statistical uncertainties in the spatial variability parameters based on the cone penetration test (CPT) dataset. The spatial variability parameters of interest include the trend function, standard deviation and scale of fluctuation for the spatial variability, and so on. In contrast to the Metropolis–Hastings (MH) algorithm, the TMCMC algorithm is a tune-free algorithm: it does not require the specification of the proposal probability density function (PDF), hence there is no need to tune the proposal PDF. Also, there is no burn-in period to worry about, and the convergence issue is mild for TMCMC because the samples spread widely. Moreover, it can estimate the model evidence, a quantity essential for Bayesian model comparison, without extra computation cost. The effectiveness for the TMCMC algorithm is demonstrated through simulated examples and a real case study. •The transitional Markov chain Monte Carlo (TMCMC) algorithm is introduced.•TMCMC is a tune-free algorithm: there is no need to specify the proposal PDF.•TMCMC can estimate model evidence as a by-product without extra computation cost.•The robustness of TMCMC is demonstrated through simulations and real case history.•Matlab codes for TMCMC are given in Appendix.