The Annals of Statistics

The problem of low counts in a signal plus noise model

Hsiuying Wang and Michael Woodroofe

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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.

Article information

Source
Ann. Statist., Volume 28, Number 6 (2000), 1561-1569.

Dates
First available in Project Euclid: 12 March 2002

Permanent link to this document
https://projecteuclid.org/euclid.aos/1015957470

Digital Object Identifier
doi:10.1214/aos/1015957470

Mathematical Reviews number (MathSciNet)
MR1835031

Zentralblatt MATH identifier
1105.62300

Subjects
Primary: 62C15: Admissibility
Secondary: 62F03: Hypothesis testing 62P35: Applications to physics

Keywords
Admissibility ancillary statistic Bayesian solutions confidence intervals neutrino oscillations $p$-values risk

Citation

Woodroofe, Michael; Wang, Hsiuying. The problem of low counts in a signal plus noise model. Ann. Statist. 28 (2000), no. 6, 1561--1569. doi:10.1214/aos/1015957470. https://projecteuclid.org/euclid.aos/1015957470


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