Abstract Details
Activity Number:
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230
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Type:
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Topic Contributed
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Date/Time:
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Monday, August 5, 2013 : 2:00 PM to 3:50 PM
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Sponsor:
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Section on Bayesian Statistical Science
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Abstract - #308231 |
Title:
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Defining Testing Priors from Estimation Priors via Truncation
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Author(s):
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David Rossell*+ and Donatello Telesca
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Companies:
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IRB Barcelona and University of California at Los Angeles
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Keywords:
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model selection ;
estimation ;
non-local prior ;
posterior sampling
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Abstract:
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Bayesians often distinguish estimation and testing priors. For testing point masses are combined with informative continuous priors, but for parameter estimation vague/improper priors seem most popular. While estimation and testing can be conciliated with decision-theoretic considerations, we argue a view from simple prior specification principles. Informative priors offer advantages for estimation, e.g. inducing regularized estimates, and are increasingly used in high-dimensional setups. Hence, we take as our starting point an informative, absolutely continuous estimation prior. To achieve a conciliation, we turn the estimation prior into a testing prior. We add point masses to capture neighborhoods around null values and truncate the continuous prior away from them. We treat the unknown truncation point as a latent variable. We provide representation theorems showing that such prior construction is equivalent to non-local priors (NLPs), a class of testing priors with good properties in high-dimensions. Besides adding intuition to the development of NLPs, our characterization facilitates extension to a wide range of models and greatly simplifies posterior sampling.
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Authors who are presenting talks have a * after their name.
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