The Validation of Approximate Bayesian Computation: Theory and Practice

Given the increased complexity of modern statistical models, current techniques for analyzing those models are being challenged, and new ways of conducting statistical inference being contemplated. Approximate Bayesian computation (ABC) is part of this evolution, beginning to feature in the toolkit of the practicing statistician, and serving as a fresh topic for academic debate and investigation. This project aims to establish the theoretical validity of ABC and to develop rigorous diagnostic methods for assessing its reliability in empirical applications. Advances on this front will have significance in all fields where complex phenomena feature and approximate methods are the only feasible way of understanding those phenomena.