A Bayesian hierarchical point process model for epidermal nerve fiber patterns

Abstract

We introduce the Thomas process in a Bayesian hierarchical setting as a model for point pattern data with a nested structure. This model is applied to a nerve fiber data set which consists of several point patterns of nerve entry points from 47 subjects divided into 3 groups, where the grouping is based on the diagnosed severity of a certain nerve disorder. The modeling assumption is that each point pattern is a realization of a Thomas process, with parameter values specific to the subject. These parameter values are in turn assumed to come from distributions that depend on which group the subject belongs to. To fit the model, we construct an MCMC algorithm, which is evaluated in a simulation study. The results of the simulation study indicate that the group level mean of each parameter is well estimated, but that the estimation of the between subject variance is more challenging. When fitting the model to the nerve fiber data, we find that the structure within clusters appears to be the same in all groups, but that the number of clusters decreases with the progression of the nerve disorder.

Keywords: Bayesian estimation; Cluster point process; Epidermal nerve fibers; Hierarchical structure; Nerve entry points; Thomas process.