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Activity Number: 351
Type: Topic Contributed
Date/Time: Tuesday, August 2, 2016 : 10:30 AM to 12:20 PM
Sponsor: Section on Bayesian Statistical Science
Abstract #319777 View Presentation
Title: Truncated Completely Random Measures
Author(s): Trevor Campbell* and Jonathan Huggins and Tamara Broderick and Jonathan How
Companies: MIT and MIT and MIT and MIT
Keywords: completely random measure ; truncation ; bayesian nonparametrics ; poisson point process

Completely random measures (CRM) and their normalizations are a rich source of Bayesian nonparametric (BNP) priors. In this paper we study three classes of sequential CRM representations that can be used for simulation and posterior inference. These representations subsume existing ones that were developed in an ad hoc manner for specific processes. Since CRMs with infinitely many atoms cannot be used in practice, sequential representations are often truncated. We provide truncation error analyses for each type of sequential representation, generalizing and improving upon existing truncation error bounds in the literature. We also provide error bounds for the normalizations of these truncated representations. We analyze the computational complexity of the sequential representations, which in conjunction with our error bounds allows us to study which representations are the most efficient. We include numerous applications of our theoretical results to popular (normalized) CRMs, demonstrating that our results provide a suite of tools that allow for the straightforward representation and analysis of CRMs that have not previously been used in a Bayesian nonparametric context.

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