In this dissertation, we develop some new spatial point process models and discuss their applications to the analysis of functional neuroimaging data. In the first project, we propose a Bayesian spatial hierarchical model using a marked independent cluster process for functional neuroimaging meta analysis. In contrast to the current approaches, our hierarchical model accounts for intra-study variation in location (if any), inter-study variation, and idiosyncratic foci that do not cluster between studies. A defining feature of our model is its ability to dissociate inter-study spread of foci from the spatial uncertainty in population centers. Our model is illustrated on a meta analysis consisting of 437 studies from 164 publications.

In the second project, motivated by joint analysis of multi type functional neuroimaging meta analysis data, we propose a non-parametric Bayesian modeling approach that extends the Poisson/Gamma random field model for multivariate point processes. In particular, each type of point patterns is modeled as a Poisson point process driven by a random intensity that is modeled as a kernel convolution of a gamma random field. The type-level gamma random fields are linked and modeled as a realization of a common gamma random field shared by all groups. We propose a hybrid algorithm with adaptive rejection sampling (ARS) embedded in a Markov chain Monte Carlo (MCMC) algorithm for posterior inference. We illustrate our models on simulated examples and two real data sets.

The aim of the third project is to produce reverse inference on psychological states given functional neuroimaging meta analysis data. Given type labels that classify each study, we construct a Bayesian spatial point process classifier based on the posterior predictive probability of class membership. We measure performance via leave-one-out cross validation using an importance sampling approach that avoids multiple posterior simulations. We demonstrate our method on the meta analysis of emotions, classifying different sub-types of emotions. Our method attains a much higher prediction accuracy compared with a comparable naive Bayesian classifier.