Random probability measures via Polya sequences: revisiting the Blackwell-MacQueen urn scheme

The continuum-of-urns scheme, generalized beta and Indian buffet processes, and hierarchies thereof

We describe the combinatorial stochastic process underlying a sequence of conditionally independent Bernoulli processes with a shared beta process hazard measure. As shown by Thibaux and Jordan [TJ07], in the special case when the underlying beta process has a constant concentration function and a finite and nonatomic mean, the combinatorial structure is that of the Indian buffet process (IBP) introduced by Griffiths and Ghahramani [GG05]. By reinterpreting the beta process introduced by Hjort [Hjo90] as a measurable family of Dirichlet processes, we obtain a simple predictive rule for the gen…

Conditionally identically distributed species sampling sequences

Conditional identity in distribution (Berti et al. (2004)) is a new type of dependence for random variables, which generalizes the well-known notion of exchangeability. In this paper, a class of random sequences, called Generalized Species Sampling Sequences, is defined and a condition to have conditional identity in distribution is given. Moreover, a class of generalized species sampling sequences that are conditionally identically distributed is introduced and studied: the Generalized Ottawa sequences (GOS). This class contains a '`randomly reinforced'' version of the Pólya urn and of the Bl…

可交换测度值Pólya序列的一些发展

Some developments of exchangeable measure-valued Pólya sequences

本文研究可交换测度值Pólya序列，证明其先验分布是Dirichlet过程混合，并扩展到包含零分量和条件同分布情形。

Baysian inference via classes of normalized random measures

One of the main research areas in Bayesian Nonparametrics is the proposal and study of priors which generalize the Dirichlet process. Here we exploit theoretical properties of Poisson random measures in order to provide a comprehensive Bayesian analysis of random probabilities which are obtained by an appropriate normalization. Specifically we achieve explicit and tractable forms of the posterior and the marginal distributions, including an explicit and easily used description of generalizations of the important Blackwell-MacQueen Pólya urn distribution. Such simplifications are achieved by th…