the multiset provide no such information to the EFPF; only the sizes of the multiset features are relevant in the EFPF case.

\[prop:efpf\] The class of exchangeable feature allocations with EFPFs is a strict but non-empty subclass of the class of exchangeable feature allocations.

below shows that the class of feature allocations with EFPFs is non-empty, and below establishes that there exist simple exchangeable feature allocations without EFPFs.

\[ex:epf\_ibp\] The Indian buffet process (IBP) [@griffiths:2006:infinite] is a generative model for a random feature allocation that is specified recursively in a manner akin to the Chinese restaurant process [@aldous:1985:exchangeability] in the case of partitions. The metaphor involves a set of “customers” that enter a restaurant and sample a set of “dishes.” Order the customers by placing them in one-to-one correspondence with the indices $n \in \mathbb{N}$. The dishes in the restaurant correspond to feature labels. Customers in the Indian buffet can sample any non-negative integer number of dishes. The set of dishes chosen by a customer $n$ is just $\indfao_{n}$, the collection of feature labels for the features to which $n$ belongs, and the procedure described below provides a way to construct $\indfao_{n}$ recursively.

We describe an extended version [@teh:2009:indian; @broderick:2012:beta] 