Conjugate Bayesian Models

This chapter defines the Bayesian conjugate property cast in a predictive statistical setting. For a given likelihood model class, certain classes of prior models exhibit the conjugate property if the associated posterior model class is identical to the prior one. This property implies the analytical tractability of the ultimate Bayesian solution, namely, the posterior model. Based on this posterior model, spatial prediction with associated quantifications of uncertainty can be obtained. Three simple instructive examples of the conjugate characteristics are presented.