Academic

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 exploring 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 inference methods. Second, we consider variational inference for performing a modified form of Bayesian inference called “cutting feedback” in situations where the model can be misspecified. Conventional Bayesian computational approaches are difficult to implement for cutting feedback methods. Both mean field and fixed form variational approximations are considered. Conflict checks are suggested to help decide whether to cut. Third, we propose to use the skew Gaussian decomposable graphical models as a new flexible family of variational approximations. With this family of approximations, marginal skewness can be captured, while the prescribed conditional independence structure based on the true posterior distribution can be imposed. To make the family more flexible, implicit copula extensions based on marginal transformations are also considered.