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Activity Number:
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362
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Type:
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Contributed
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Date/Time:
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Wednesday, August 6, 2008 : 8:30 AM to 10:20 AM
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Sponsor:
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Section on Bayesian Statistical Science
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| Abstract - #302394 |
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Title:
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Comparison of the Bayesian Prediction Limits for the Poisson Distribution
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Author(s):
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Valbona Bejleri*+ and Alexander White
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Companies:
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University of the District of Columbia and Texas State University, San Marcos
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Address:
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4200 Connecticut Avenue, N.W., Washington, DC, 20008,
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Keywords:
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Jeffreys' prior ; noninformative ; lower limit ; uniform prior ; frequentist
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Abstract:
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Bayesian limits for the Poisson distribution with informative and noninformative priors are compared based on their frequentist properties. We show that the modified Jeffreys' prior is the only prior that gives the optimal (largest) Bayesian lower prediction limit which coincides asymptotically with the frequentist lower prediction limit. The upper prediction limit derived from it does not always coincide with the frequentist one. For any other prior, the optimal Bayesian lower limit is either smaller than the one derived based on the modified Jeffreys' prior, or the frequency of making a wrong prediction exceeds the probability of wrong coverage. Similar results are obtained for the upper prediction limit when uniform prior is assigned on the parameter. There is no prior distribution such that the upper and lower Bayesian limits always coincide with the frequentist limits.
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