Reliability based Bayesian inference for probabilistic classification: An overview of sampling schemes

Abstract

As physical systems have become more complex, the demand for models which incorporate uncertainties in the systems behavior has grown. Bayesian updating is a powerful method which allows models to be learned as new information and data becomes available. In a high dimensional setting, Bayesian updating requires the computation of an integral which is analytically intractable. Markov Chain Monte Carlo (MCMC) techniques include a popular class of methods to solve such an integral. A disadvantage of MCMC however, is its low computational efficiency for problems with many uncertain parameters. Accordingly, a relation between the Bayesian updating problem and the engineering reliability problem has been established. The BUS (Bayesian Updating with Structural Reliability Methods) approach enables reliability methods which are efficient in high dimensions, but retain the advantages of MCMC, to be applied to Bayesian updating problems. Subset Simulation (SuS) is an efficient Monte Carlo technique suitable for such tasks. The BUS algorithm requires a likelihood multiplier to be calculated prior to implementation of SuS. The issue of correctly choosing a suitable multiplier value has gathered much interest. Consequently, a modified BUS framework has been developed which computes the multiplier automatically. The choice of MCMC algorithm within SuS greatly affects sample quality, model efficiency and sample acceptance rate. A low sample acceptance rate results in many repeated samples and thus low efficiency. As such this research investigates the effect of different sampling schemes within the SuS algorithm on the performance of the modified BUS framework for binary probabilistic classification models.