Uniformly Hyper-Efficient Bayes Inference in a Class of Nonregular Problems

Date
2009-01-01
Authors
Nordman, Danial
Vardeman, Stephen
Bingham, Melissa
Vardeman, Stephen
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Abstract

We present a tractable class of nonregular continuous statistical models where 1) likelihoods have multiple singularities and ordinary maximum likelihood is intrinsically unavailable, but 2) Bayes procedures achieve convergence rates better than n−1 across the whole parameter space. In fact, for every p>1, there is a member of the class for which the posterior distribution is consistent at rate n−puniformly in the parameter.

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<p>This is an Accepted Manuscript of an article published by Taylor & Francis in The American Statistician in 2009, available online: <a href="http://www.tandfonline.com/10.1198/tast.2009.08170" target="_blank">http://www.tandfonline.com/10.1198/tast.2009.08170.</a></p>
Keywords
Circular distributions, Credible interval, Nonregular convergence rates
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