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,

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... ed in part on our new Poisson process construction. Recently, a stick-breaking construction of the full beta process was derived by Paisley et al. (2010) . The derivation relied on a limiting process involving finite matrices, similar to the limiting process used to derive the IBP. However, the