Statistical modelling using product partition models

Product partition models (PPMs) allow us to partition a set of objects into k sets. PPMs are a special case of Bayesian Partition models. They use partially exchangeable priors where given a partition ρ of the objects into k sets, the objects in the same set are exchangeable and the objects belonging to distinct sets are independent. PPMs specify prior probabilities for a random partition and update these into posterior distributions of the same form. They provide a convenient way of allowing the data to weight the partitions likely to hold. Posterior estimates of the parameter of interest are obtained by conditioning on the partition and averaging over all generated partitions. Markov chain Monte Carlo (MCMC) techniques are used to generate partitions of the data. PPMs can be applied to many diverse estimation problems and in this paper we outline two areas where they are useful.