Bayesian Modeling of Marked Spatial Point Patterns

• Activity Number: 350
• Type: Topic Contributed
• Date/Time: Wednesday, August 10, 2005 : 8:30 AM to 10:20 AM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Matthew Bognar*+
• Companies: The University of Iowa
• Keywords: marked spatial point pattern ; Bayesian inference ; Markov chain Monte Carlo (MCMC) ; pairwise interacting point process ; mark chemical activity function

Abstract

Many analyses of (continuously) marked spatial point patterns assume the density of points, with differing marks, is identical. However, as noted in the originative paper of Goulard, S{\"a}rkk{\"a}, and Grabarnik (1996), such an assumption is not realistic in many situations. For example, a stand of forest may have many more small trees than large, hence the model should allow for a higher density of points with small marks. In addition, as suggested by Ogata and Tanemura (1985), the interaction between points should be a function of their mark, allowing, for example, the range of interaction for large trees to exceed that of smaller trees. The aforementioned articles use frequentist inferential techniques, but interval estimation presents difficulties due to the complex distributional properties of the estimates. We suggest the use of Bayesian inferential techniques. While a Bayesian approach requires a complex, computational implementation of (reversible jump) MCMC methodology, we are able to obtain a wider variety of inferences (including interval estimates). We demonstrate our approach by analyzing the well-known spruce dataset using a hard-core Straussian model.