APPROXIMATE INFERENCE FOR COMPLEX MODELS

Abstract

Bayesian methods are attractive for large datasets and complex models. However, in complicated settings, Bayesian computation is challenging with conventional Monte Carlo approaches. To overcome this problem, there is much recent interest in approximate inference methods. This thesis makes three contributions in this area.

First, we develop a moment-based assessment and adjustment method to improve estimation by approximate methods. Second, we consider variational inference for performing a modified Bayesian inference called “cutting feedback” in situations where the model can be misspecified. Conventional Bayesian computational approaches are difficult to implement. We consider variational approximations and suggest conflict checks to help decide whether to cut. Third, we propose a new flexible variational approximation family: the skew Gaussian decomposable graphical models. With this family, marginal skewness can be captured, while the prescribed conditional independence structure based on the true posterior can be imposed. Implicit copula extensions based on marginal transformations are also considered.