Sequential Methods in Approximate Bayesian Computation

Abstract

This thesis concentrates on improving on existing methodology for sequential Monte Carlo (SMC) algorithms within Approximate Bayesian Computation.
Approximate Bayesian Computation (ABC) provides a methodology for estimating the posterior distribution of parameters θ, given observed data y, in cases where the likelihood function is intractable, provided one can simulate data under the model of interest. ABC algorithms can be highly computationally expensive to implement, due to the large number of model simulations required. This thesis gives alterations to the SMC-ABC algorithm of Del Moral et al. [1], which aim to reduce the computational cost and level of user tuning required in within ABC. Furthermore, the accuracy of the estimated posterior distribution is sensitive to the way in which the data, y is summarised and optimal summary statistics are unknown for non-trivial models. This thesis proposes an iterative method for selecting summary statistics, which is implemented within an SMC-ABC algorithm.
Recently there has been a move towards empirically modelling the likelihood function, within the ABC literature.
In the final chapter of this theses, we present two algorithms which use density estimation to model the likelihood, and show that this has the potential to dramatically reduce the computational cost of ABC, by lowering the number of model simulations required.

Date of Award	20 Mar 2018
Original language	English
Awarding Institution	University of Bristol
Supervisor	Mark A Beaumont (Supervisor)