Research on Approximate Bayesian Computation

This thesis presents the development of a new numerical algorithm for statistical inference problems that require sampling from distributions which are intractable. We propose to develop our sampling algorithm based on a class of Monte Carlo methods, Approximate Bayesian Computation (ABC), which are specifically designed to deal with this type of likelihood-free inference. ABC has become a fundamental tool for the analysis of complex models when the likelihood function is computationally intractable or challenging to mathematically specify. The central theme of our approach is to enhance the current ABC algorithms by exploiting the structure of the mathematical models via derivative information. We introduce Progressive Correction of Gaussian Components (PCGC) as a computationally efficient algorithm for generating proposal distributions in our ABC sampler. We demonstrate on two examples that our new ABC algorithm has an acceptance rate that is one to two orders of magnitude better than the basic ABC rejection sampling