An MCMC algorithm for bayesian analysis of Hierarchical Partition Models

Summary

The paper proposes an MCMC algorithm to derive the posterior distribution of the different partially exchangeable structures (models) involved in a Hierarchical Partition Model (HPM). The suggested procedure operates only on the discrete space of the models since it is possible to compute the posterior distribution of the parameters in an exact way for each given model. The performance of the algorithm is discussed in details and it appears satisfactory both when the number of possible models is small or huge. However, in the latter case too many models are typically singled out because the likelihood is essentially constant over them; this suggests the necessity of some form of aa priori model pruning.