Proceedings of the
8th International Symposium on Geotechnical Safety and Risk (ISGSR)
14 – 16 December 2022, Newcastle, Australia
Editors: Jinsong Huang, D.V. Griffiths, Shui-Hua Jiang, Anna Giacomini, Richard Kelly
doi:10.3850/978-981-18-5182-7_07-010-cd
Bayesian Gaussian Mixture Model Learning with Subset Simulation
1Engineering Risk Analysis Group, Technische Universität München, Arcisstr. 21, 80290 München, Germany.
2MOE Key Laboratory of High-Speed Railway Engineering, Institute of Smart City and Intelligent Transportation, Southwest Jiaotong University, Chengdu 611756, P. R. China
ABSTRACT
The Gaussian mixture model (GMM) provides a convenient and flexible means for probabilistic modelling of geotechnical parameters. We employ the Bayesian approach for fitting GMMs to data, which enables quantifying the uncertainty of GMM parameter estimates and selecting the number of components in the mixture through comparing the marginal likelihood of the data (aka evidence) for each model. To solve the Bayesian updating problem and estimate the marginal likelihood, we develop a variant of the adaptive BUS (Bayesian Updating with Structural reliability methods) algorithm that effectively explores all modes of the posterior distribution. The latter is achieved through the implementation of an adaptive Markov chain Monte Carlo sampler within subset simulation-based BUS, termed elliptical slice sampler. We demonstrate the effectiveness of the proposed method with a univariate geotechnical dataset taken from the ISSMGE TC304 database.
Keywords: Gaussian mixture model, Bayesian learning, model selection, aBUS, elliptical slice sampling.
