The Stick-Breaking Construction of the Beta Process as a Poisson Process

Details The Stick-Breaking Construction of the Beta Process as a Poisson Process The Stick-Breaking Construction of the Beta Process as a Poisson Process

2011-09-02

arxiv.org/abs/1109.0343v2

Mathematics

Statistics Theory

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Scientific paper

We show that the stick-breaking construction of the beta process due to Paisley, et al. (2010) can be obtained from the characterization of the beta process as a Poisson process. Specifically, we show that the mean measure of the underlying Poisson process is equal to that of the beta process. We use this underlying representation to derive error bounds on truncated beta processes that are tighter than those in the literature. We also develop a new MCMC inference algorithm for beta processes, based in part on our new Poisson process construction.

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