2017-06-21

# Bayesian subset simulation

## Prof. Julien Bect, CentraleSupélec, France

17 Jul 2017, 16:15–17:45; Location: S2|17-103

The numerical computation of small probabilities of failure for a system is a notoriously difficult problem, and the Subset Simulation algorithm of Au & Beck (Prob. Eng . Mech., 2001) has become one of the most popular method to solve it. Subset simulation has been shown to provide significant savings in the number of evaluations of the performance functions, with respect to a brute-force Monte Carlo approach. The number of evaluations remains quite high, however, for many practical applications where the performance function $$f$$ is provided by an expensive-to-evaluate computer model.

This seminar will focus a stochastic algorithm, called Bayesian subset simulation (BSS), that uses a blend of ideas from the subset simulation approach and from the sequential design of computer experiments based on Gaussian process (GP) models. A key idea, as in the subset simulation algorithm, is to estimate the probabilities of a sequence of excursion sets of $$f$$ above intermediate thresholds, using a sequential Monte Carlo (SMC) approach. A GP prior on $$f$$ is used to define the sequence of densities targeted by the SMC algorithm, and drive the selection of evaluation points of $$f$$ to estimate the intermediate probabilities. Adaptive procedures are proposed to determine the intermediate thresholds and the number of evaluations to be carried out at each stage of the algorithm.

We will discuss the main ideas behind the method and present a free software implementation for Matlab/Octave (using the STK toolbox) that makes it easy for you to try BSS on your own problems.

Main ref: Julien Bect, Ling Li and Emmanuel Vazquez. Bayesian subset simulation. https://arxiv.org/abs/1601.02557. SIAM Journal on Uncertainty Quantification (accepted).

Category: CE Seminar