Bayesian Inference and Computing for Spatial Point Patterns

This monograph results from a CBMS short course given by Alan Gelfand at the University of California at Santa Cruz the week of August 14-18, 2017. It extracts a portion of the lecture material which focuses on spatial point patterns and substantially expands it, in addition to providing introductory material (Chapter 1). The decision to focus on spatial point pattern models reflects the fact that this area of spatial analysis has, arguably, received the least attention in the literature and, even less within the Bayesian community. At this point, the other, more mainstream spatial and spatio-temporal material is discussed and readily available in many books. The monograph provides a forum for presentation of novel Bayesian inference and model fitting material which has been very recently developed by Gelfand and collaborators. This material is predicated on an assumption which currently drives much Bayesian work: if you can fit a Bayesian model and if you can simulate realizations of the model, you can do full Bayesian inference under the model.