Abstract
This thesis is concerned with asymptotic methods for Bayesian computation. Both the theory and the practice of these methods are discussed. Some of the methods are modifications of Bayesian Bartlett corrections, posterior expectations and predictive densities based on signed root log-likelihood ratios obtained in Sweeting (1996) that are designed to address some difficulties that arise in applying these asymptotics in multiparameter problems. Others explore the use of hybrid methods involving data augmentation, importance sampling, control variates and asymptotics. The ultimate goal will be to provide a complete package for estimating univariate posterior distribution functions, posterior density functions, posterior moments and marginal posterior densities, including checks on the accuracy of these estimators. Although the real value of the methods described here is that they can be applied to multiparameter problems, for each method the theory is developed first for the single parameter case in order to expose the main ideas. An appealing feature of these methods is that log-likelihood derivatives beyond second order are not required. The power and the limitations of the methods are illustrated by means of examples.