DMS 9626819 Wolpert Bayesian hierarchical models are introduced to account for uncertainty and spatial variation in the underlying intensity measure for point process models. Inhomogeneous gamma process random fields and, more generally, Markov random fields with infinitely-divisible distributions are used to construct positively autocorrelated intensity measures for spatial Poisson point processes, used in turn to model the number and location of individual events. A data augmentation scheme and Markov chain Monte Carlo numerical methods are employed to generate samples from Bayesian posterior and predictive distributions. The methods are developed in both continuous and discrete settings, and are applied to problems in forest ecology and other fields. Spatial patterns are an important aspect of statistical data in many fields of investigation-- disease mapping, where spatial patterns may help us learn about causes or patterns of susceptibility to specific diseases; agriculture, where spatial patterns, influenced by soil types, economics, and regional agricultural traditions, may help us predict yield; and forest management, where spatial patterns help us learn about past land-use and help us anticipate problems (for example, susceptibility to insect infestations) and management opportunities (the harvesting of overly populous species). The present research exploits recent advances in computing hardware and algorithms and in mathematical probability theory to develop new and better statistical models and numerical algorithms for exploring spatial pattern data. The new statistical models and numerical algorithms are applied to problems in the Environment (studying changing patterns of forest speciation and biodiversity in this Federal Strategic Area), Disease Mapping, and Transportation Theory (helping to predict commuter traffic flow in an evolving urban environment, supporting the Federal Strategic Area of Civil Infrastructure).
