The problem of low counts in a signal plus noise model
Hsiuying Wang, Michael Woodroofe
The Annals of Statistics · 2000 · Volume 28 · Issue 6
Abstract
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.
Keywords
$P$-values, 62C15, 62F03, 62P35, Admissibility, ancillary statistic, Bayesian solutions, confidence intervals, neutrino oscillations, risk
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