ABSTRACT
As we noted in Chapter 1, point patterns form the third type of spatial data that we collect. Of the three data types, in our view, spatial and space-time point patterns are the least developed in terms of Bayesian development and application. There is a consequential formal theoretical literature and there is by now a substantial body of exploratory tools. We shall explore both of these parts in Sections 8.2 and 8.3. In Section 8.4 we look at basic modeling specifications. Here, it is evident that in the modeling side, in particular, the hierarchical approach through fully Bayesian modeling has received much less attention. In Section 8.5 we take up the problem of generating point patterns, potentially useful for simulation-based model fitting. In Section 8.6 we extend the class of models to NeymanScott and Gibbs processes, again, with an eye toward Bayesian model fitting. In Section 8.7 we consider marked point processes. Section 8.8 will look at space-time point patterns, i.e., how can we learn about the evolution of point patterns in time? We conclude in Section 8.9 with a few special topics, arguably, areas which need more development for the practitioner. Several exercises are presented at the end. Also, we believe that the inferential aspects of this chapter will be best appreciated after absorbing Chapters 5 and 6.
