Bayesian Spatial Modelling

This chapter contains a discussion of the characteristics of spatial variables. High-dimensional spatial discretisation, single-realisation inference and complex observation acquisition procedures are merely some of these characteristics. Bayes’ rule is presented as the fundamental principle for spatial modelling. The likelihood model represents the observation collection design, whereas the prior model represents expert knowledge and experience. Jointly, these models uniquely define the ultimate solution to Bayesian modelling: the posterior model. The spatial variable is defined to be one of three types: continuous, event and mosaic. Motivating examples of modelling each of these spatial variable types are given. Simulation algorithms suitable for assessing this posterior model are presented in detail. Lastly, the notation in the book is established.