Tools for Statistical Inference

The goal of this book is to provide a unified presentation of a variety of algorithms for likelihood and Bayesian inference. Two types of methods are considered: observed data and data augmentation methods. The observed data methods, which are applied directly to the likelihood or posterior inference, include maximum likelihood, Laplace expansion, Monte Carlo and importance sampling. The data augmentation methods rely on an augmentation of the data which simplifies the likelihood or posterior inference. These include EM, Louis' modification of the EM, poor man's data augmentation, SIR and the Gibbs sampler.