Institute of Mathematical Statistics Lecture Notes - Monograph Series

Existence of the signal in the signal plus background model

Tonglin Zhang

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Searching for evidence of neutrino oscillations is an important problem in particle physics. Suppose that evidence for neutrino oscillations from an LSND experiment reports a significant positive oscillation probability, but that the LSND result is not confirmed by other experiments. In statistics, such a problem can be proposed as the detection of signal events in the Poisson signal plus background model. Suppose that an observed count $X$ is of the form $X=B+S$, where the background $B$ and the signal $S$ are independent Poisson random variables with parameters $b$ and $\theta$ respectively, $b$ is known but $\theta$ is not. Some recent articles have suggested conditioning on the observed bound for $B$; that is, if $X=n$ is observed, the suggestion is to base the inference on the conditional distribution of $X$ given $B\le n$. This suggestion is used here to derive an estimator of the probability of the existence of the signal event. The estimator is examined from the view of decision theory and is shown to be admissible.

Chapter information

Jiayang Sun, Anirban DasGupta, Vince Melfi, Connie Page, eds., Recent Developments in Nonparametric Inference and Probability: Festschrift for Michael Woodroofe (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2006), 144-155

First available in Project Euclid: 28 November 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62C15: Admissibility
Secondary: 62C10: Bayesian problems; characterization of Bayes procedures 62F25: Tolerance and confidence regions 62F03: Hypothesis testing

admissible coverage probability credible and confidence intervals maximum likelihood estimator mean squared error signal plus background Type I error rate

Copyright © 2006, Institute of Mathematical Statistics


Zhang, Tonglin. Existence of the signal in the signal plus background model. Recent Developments in Nonparametric Inference and Probability, 144--155, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2006. doi:10.1214/074921706000000653.

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