Approximate Bayesian Computation by Subset Simulation

TL;DR

This paper introduces ABC-SubSim, a novel algorithm combining Approximate Bayesian Computation with Subset Simulation to improve efficiency in Bayesian updating, especially for rare-event scenarios, demonstrated through real-world examples.

Contribution

The paper presents a new ABC algorithm that integrates Subset Simulation, enhancing computational efficiency and providing evidence estimates for model assessment.

Findings

ABC-SubSim outperforms recent ABC algorithms in efficiency

It achieves comparable or better accuracy in posterior estimation

Provides estimates of model evidence as a by-product

Abstract

A new Approximate Bayesian Computation (ABC) algorithm for Bayesian updating of model parameters is proposed in this paper, which combines the ABC principles with the technique of Subset Simulation for efficient rare-event simulation, first developed in S.K. Au and J.L. Beck [1]. It has been named ABC- SubSim. The idea is to choose the nested decreasing sequence of regions in Subset Simulation as the regions that correspond to increasingly closer approximations of the actual data vector in observation space. The efficiency of the algorithm is demonstrated in two examples that illustrate some of the challenges faced in real-world applications of ABC. We show that the proposed algorithm outperforms other recent sequential ABC algorithms in terms of computational efficiency while achieving the same, or better, measure of ac- curacy in the posterior distribution. We also show that ABC-SubSim readily provides an estimate of the evidence (marginal likelihood) for posterior model class assessment, as a by-product.