Similarity analysis in Bayesian random partition models

This work proposes a method to assess the influence of individual observations in the clustering generated by any process that involves random partitions. We call it Similarity Analysis. It basically consists of decomposing the estimated similarity matrix into an intrinsic and an extrinsic part, coupled with a new approach for representing and interpreting partitions. Individual influence is associated with the particular ordering induced by individual covariates, which in turn provides an interpretation of the underlying clustering mechanism. We present applications in the context of Species Sampling Mixture Models (SSMMs), including Bayesian density estimation and dependent linear regression models.