WEIGHTED CHINESE RESTAURANT PROCESSES

A class of distributions on partitions of a finite collection of objects is defined. The probability of a specific partition is a product of functions of clusters of the partition with the product running over all clusters. This class contains Chinese restaurant processes as a special case. The simulation of a distribution in this class is described through the seating probability that gives the conditional probability of joining a new object to an existing cluster. Examples in Bayesian mixture models are given.