Keywords: Bayesian nonparametrics, Approximations, Pitman--Yor process, Gibbs-type priors
Abstract: In Bayesian nonparametrics, knowledge of the prior distribution induced on the number of clusters is key for prior specification and calibration. However, evaluating this prior is infamously difficult even for moderate sample size. We evaluate several statistical approximations to the prior distribution on the number of clusters for Gibbs-type processes, a class including the Pitman--Yor process and the normalized generalized gamma process. We introduce a new approximation based on the predictive distribution of Gibbs-type process, which compares favourably with the existing methods. We thoroughly discuss the limitations of these various approximations by comparing them against an exact implementation of the prior distribution of the number of clusters.