A Bayesian mixture model to quantify parameters of spatial clustering

A new Bayesian approach for quantifying spatial clustering is proposed that employs a mixture of gamma distributions to model the squared distance of points to their second nearest neighbors. The method is designed to answer questions arising in biophysical research on nanoclusters of Ras proteins. It takes into account the presence of disturbing metacluster structures as well as non-clustering objects, both common among Ras clusters. Its focus lies on estimating the proportion of points lying in clusters, the mean cluster size and the mean cluster radius without depending on prior knowledge of the parameters. The performance of the model compared to other cluster methods is demonstrated in a comprehensive simulation study, employing a specific new class of spatial point processes, the double Matérn cluster process. Further results and arguments as well as data and code are available as supplementary material.