## The Annals of Statistics

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

### The problem of low counts in a signal plus noise model

Hsiuying Wang and Michael Woodroofe

#### 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