Doubly stochastic 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 process...

An auxiliary variable method which we refer to as a slice Gibbs sampler is shown to provide an attractive simulation-based model tting strategy for tting Bayesian models under proper priors. Though broadly applicable, we illustrate in the context of tting spatial models for geo-referenced or point source data. Spatial modeling within a Bayesian framework ooers inferential advantages and the sli...

In this paper, we propose a novel symmetrical EEG/fMRI fusion method which combines EEG and fMRI by means of a common generative model. We use a total variation (TV) prior to model the spatial distribution of the cortical current responses and hemodynamic response functions, and utilize spatially adaptive temporal priors to model their temporal shapes. The spatial adaptivity of the prior model ...

We consider the problem of designing a network of sampling locations in a spatial domain that will be used to interpolate a spatial field. We focus on the random field model in which variance is given by an unknown step function of the locations. We express this uncertainty through an appropriate class of prior distributions and introduce a Bayesian sequential sampling algorithm. At each step, ...