Abstract

We discuss some nonparametric Bayesian mixture models for spatial point processes with applications in biological contexts. We first describes and develops models for spatial point processes in which the point outcomes are latent, where indirect observations related to the point outcomes are available, and in which the underlying spatial intensity functions are typically highly heterogenous. Spatial intensities of inhomogeneous Poisson processes are represented via flexible nonparametric Bayesian mixture models. Examples drawn from immunofluorescence histology analysis in biological studies, demonstrate the modelling approach and computational methodology. We also discuss dynamic spatial mixture modeling for inhomogeneous point processes. A time varying spatial Dirichlet process Gaussian mixture model is proposed to characterize the underling dynamic of intensity of the spatial inhomogeneous point process. We illustrate this approach via simulation examples of extended target tracking and cell fluorescent microscopic imaging tracking.