Statistics Seminar: Min Ngoc Tran (USyd) -- Exact Bayesian Inference for Approximate Bayesian Computation

Abstract: Approximate Bayesian Computation (ABC) is a powerful method for carrying 
out Bayesian inference when the likelihood is computationally intractable. However, 
a drawback of ABC is that it is an approximate method that suffers from a systematic 
error because it is necessary to set a tolerance level to make the computation 
tractable. The issue of how to optimally set this tolerance level has been the 
subject of extensive research. We propose an ABC algorithm based on importance 
sampling that estimates expectations with respect to the exact posterior distribution 
given the observed summary statistics. This overcomes the need to select the tolerance 
level. By exact we mean that there is no systematic error and the Monte Carlo can be 
made arbitrarily small by increasing the number of importance samples. We provide a 
formal justification for of the method and study its convergence properties. The 
method is illustrated in two applications and the empirical results suggest that the 
proposed ABC based estimators consistently converge to the true values as the number 
of importance samples increases.

This is joint work with Robert Kohn (UNSW).