A Bayesian hierarchical point process model for epidermal nerve fiber patterns

• Published in: Mathematical biosciences Vol. 313; pp. 48 - 60
• Main Authors: Andersson, C., Rajala, T., Särkkä, A.
• Format: Journal Article
• Language: English
• Published: United States Elsevier Inc 01.07.2019; Elsevier Science Ltd
• Subjects: Adult; Algorithms; Bayes Theorem; Bayesian analysis; Bayesian estimation; Cluster point process; Clusters; Computer simulation; Diabetic Neuropathies; Epidermal nerve fibers; Epidermis - innervation; Hierarchical structure; Humans; Matematik; Mathematical models; Mathematical sciences; Models, Biological; Models, Statistical; Nerve entry points; Nerve Fibers; Parameter estimation; Process parameters; Simulation; Thomas process; Nerve entry points; Bayesian estimation; Epidermal nerve fibers; Cluster point process; Hierarchical structure; Thomas process
• ISSN: 0025-5564; 1879-3134; 1879-3134
• DOI: 10.1016/j.mbs.2019.04.010

•Thomas process captures the clustering properties of the nerve fiber point patterns.•Hierarchical modeling gives new insight into differences between disease groups.•The number of clusters tends to decrease with the progression of neuropathy.•Neuropathy does not seem to affect the within cluster structure.•Increased clustering appears to be due to fewer nerve fiber clusters. 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.