Product partition models with correlated parameters

Abstract

In sequentially observed data, Bayesian partition models aim at partitioning the entire observation period into disjoint clusters. Each cluster is an aggregation of sequential observations and a simple model is adopted within each cluster. The main inferential problem is the estimation of the number and locations of the clusters. We extend the well-known product partition model (PPM) by assuming that observations within the same cluster have their distributions indexed by correlated and different parameters. Such parameters are similar within a cluster by means of a Gibbs prior distribution. We carried out several simulations and real data set analyses showing that our model provides better estimates for all parameters, including the number and position of the temporal clusters, even for situations favoring the PPM. A free and open source code is available.