Introduction

This introduction presents an overview of the key concepts discussed in the subsequent chapters of this book. The book is concerned with areal unit data such as the infant death counts shown. It devotes to statistical inference, in particular estimation of the model parameters. The book devotes to gridded data such as the coal ash measurements displayed. It discusses the strong assumptions on mean and semi-variogram are relaxed. A maximum likelihood theory is developed for Poisson processes, whilst the maximum pseudo-likelihood and Monte Carlo maximum likelihood methods apply more generally. The maximum likelihood equations are derived for a Gaussian autoregression model. For most other models, the likelihood is available only up to a parameter dependent normalisation constant. A simple kriging procedure is developed that is appropriate when both the mean and the semi-variogram are known explicitly. Universal kriging is apt when explanatory variables are available to define a spatial regression for the mean.