ROBUSTIFYING SEQUENTIAL NEURAL POSTERIOR ESTIMATION

Abstract

For complex statistical models, calculation of the likelihood function can sometimes be impractical. However, if data can be simulated from the model for any value of the model parameter, then it is possible to perform Bayesian inference using likelihood-free inference methods which avoid likelihood calculations. Because likelihood-free methods are used in complex situations where model understanding is difficult, there is often a risk of model misspecification that can negatively impact model-based inference and decision-making. This means it is important to develop likelihood-free methods which are robust to model misspecification. There has been much recent work on dealing with model misspecification for traditional likelihoodfree inference approaches such as approximate Bayesian computation (ABC) and synthetic likelihood, but only limited discussion of the problem in the context of neural methods which are becoming more popular. The purpose of this thesis is to investigate ways to robustify likelihood-free inference for sequential neural posterior estimation (SNPE) algorithms. A new approach to this problem is suggested, and its performance investigated in some benchmark real and simulated examples.