Redundancy of Exchangeable Estimators

Exchangeable random partition processes are the basis for Bayesian approaches to statistical inference in large alphabet settings. On the other hand, the notion of the pattern of a sequence provides an information-theoretic framework for data compression in large alphabet scenarios. Because data com...

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Bibliographic Details
Published in:Entropy (Basel, Switzerland) Switzerland), 2014-10, Vol.16 (10), p.5339-5357
Main Authors: Santhanam, Narayana P, Sarwate, Anand D, Woo, Jae Oh
Format: Article
Language:English
Subjects:
Alphabets
Bayesian analysis
Chinese restaurant process
Compressing
Data compression
Estimators
Exchange
exchangeability
Pitman–Yor process
random exchangeable partitions
Redundancy
Samples
strong and weak universal compression
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Summary:Exchangeable random partition processes are the basis for Bayesian approaches to statistical inference in large alphabet settings. On the other hand, the notion of the pattern of a sequence provides an information-theoretic framework for data compression in large alphabet scenarios. Because data compression and parameter estimation are intimately related, we study the redundancy of Bayes estimators coming from Poisson-Dirichlet priors (or "Chinese restaurant processes") and the Pitman-Yor prior. This provides an understanding of these estimators in the setting of unknown discrete alphabets from the perspective of universal compression. In particular, we identify relations between alphabet sizes and sample sizes where the redundancy is small, thereby characterizing useful regimes for these estimators.
ISSN:1099-4300
1099-4300
DOI:10.3390/e16105339