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December2000 The problem of low counts in a signal plus noise model
Hsiuying Wang, Michael Woodroofe
Ann. Statist. 28(6): 1561-1569 (December2000). DOI: 10.1214/aos/1015957470


Consider the model $X = B + S$, where $B$and $S$ are independent Poisson random variables with means $\mu$ and $\nu$, $\nu$ is unknown, but $\mu$ is known. The model arises in particle physics and some recent articles have suggested conditioning on the observed bound on $B$; that is, if $X = n$ is observed, then the suggestion is to base inference on the conditional distribution of $X$ given $B \leq n$. This conditioning is non-standard in that it does not correspond to a partition of the sample space. It is examined here from the view point of decision theory and shown to lead to admissible formal Bayes procedures.


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Hsiuying Wang. Michael Woodroofe. "The problem of low counts in a signal plus noise model." Ann. Statist. 28 (6) 1561 - 1569, December2000.


Published: December2000
First available in Project Euclid: 12 March 2002

zbMATH: 1105.62300
MathSciNet: MR1835031
Digital Object Identifier: 10.1214/aos/1015957470

Primary: 62C15
Secondary: 62F03 , 62P35

Keywords: $P$-values , Admissibility , ancillary statistic , Bayesian solutions , confidence intervals , neutrino oscillations , risk

Rights: Copyright © 2000 Institute of Mathematical Statistics


Vol.28 • No. 6 • December2000
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