Adaptive approximate Bayesian computation

TL;DR

This paper introduces an adaptive importance sampling approach for approximate Bayesian computation that reduces bias and improves efficiency, demonstrated through a population genetics example.

Contribution

It presents a novel adaptive ABC algorithm based on importance sampling and population Monte Carlo, addressing bias issues in previous methods.

Findings

Outperforms existing ABC methods in a population genetics case study

Reduces bias in posterior approximation compared to earlier techniques

Includes automatic kernel scaling for improved efficiency

Abstract

Sequential techniques can enhance the efficiency of the approximate Bayesian computation algorithm, as in Sisson et al.'s (2007) partial rejection control version. While this method is based upon the theoretical works of Del Moral et al. (2006), the application to approximate Bayesian computation results in a bias in the approximation to the posterior. An alternative version based on genuine importance sampling arguments bypasses this difficulty, in connection with the population Monte Carlo method of Cappe et al. (2004), and it includes an automatic scaling of the forward kernel. When applied to a population genetics example, it compares favourably with two other versions of the approximate algorithm.