Introduction

This introduction presents an overview of the key concepts discussed in the subsequent chapters of this book. The book reviews the Bayesian theory. It discusses why we might want to use integrated nested Laplace approximations (INLA) in preference to the alternatives. The book discusses the defaults and the choice of prior in great detail. INLA applies to a wide class of models called Latent Gaussian Models. Membership of this class requires that some parameters in the model have priors with a Gaussian distribution. The book provides merely a short tour through the ideas and methods. It considers the most general example of the MCMCglmm package of Hadfield which will handle a good subset of the models. The book describes how methods of quadrature and the Laplace approximation in particular can be used to produce accurate approximations. In statistics, these methods started from the seminal paper of Tierney and Kadane.