  Clustering of proteins is of interest in cancer cell biology. This article
proposes a hierarchical Bayesian model for protein (variable) clustering
hinging on correlation structure. Starting from a multivariate normal
likelihood, we enforce the clustering through prior modeling using angle based
unconstrained reparameterization of correlations and assume a truncated Poisson
distribution (to penalize the large number of clusters) as prior on the number
of clusters. The posterior distributions of the parameters are not in explicit
form and we use a reversible jump Markov chain Monte Carlo (RJMCMC) based
technique is used to simulate the parameters from the posteriors. The end
products of the proposed method are estimated cluster configuration of the
proteins (variables) along with the number of clusters. The Bayesian method is
flexible enough to cluster the proteins as well as the estimate the number of
clusters. The performance of the proposed method has been substantiated with
extensive simulation studies and one protein expression data with a hereditary
disposition in breast cancer where the proteins are coming from different
pathways.
