Abstract/Summary

This thesis is concerned with Monte Carlo methods for intractable and doubly intractable density estimation. The primary focus is on the likelihood free method of Approximate Bayesian inference, where the presence of an intractable likelihood term necessitates the need for various approximation procedures. We propose a novel Sequential Monte Carlo based algorithm and demonstrate the significant efficiency (computational and statistical) improvements compared to the widely used SMC-ABC, in numerical experiments for a simple Gaussian model and a more realistic random network model. Further, we investigate a recently proposed algorithm, called SAMC-ABC, an adaptive MCMC algorithm where we also demonstrate some advantages over ABC-MCMC; primarily in the reduction of variance of the estimated means although at a cost of increased bias for which we propose a potential correction. In addition, we provide theoretical guarantees of ergodicity and convergence of another newly proposed algorithm termed Adaptive Noisy Exchange, that is aimed at problems of intractable normalising constants where regular MCMC cannot be employed. Finally, we propose potential improvements and future research directions for all of the considered algorithms.