can be viewed as asserting that the indices used to label the data points are irrelevant for inference, and as such is often a natural modeling assumption. Under such an assumption, one is licensed by de Finetti’s theorem [@de_finetti:1931:funzione] to propose the existence of an underlying parameter that renders the data conditionally independent and identically distributed (iid) and to place a prior distribution on that parameter. Moreover, the theory of infinitely exchangeable sequences has advantages of simplicity over the theory of finite exchangeability, encouraging modelers to take a nonparametric stance in which the underlying “parameter” is infinite dimensional. Finally, the development of algorithms for posterior inference is often greatly simplified by the assumption of exchangeability, most notably in the case of Bayesian nonparametrics, where models based on the Dirichlet process and other combinatorial priors became useful tools in practice only when it was realized how to exploit exchangeability to develop inference procedures [@escobar:1994:estimating].

The connection of exchangeability to Bayesian nonparametric modeling is well established in the case of models for clustering. The goal of a clustering procedure is to infer a partition of the data points. In the Bayesian setting, one works with random partitions, and, under an exchangeability assumption, 