The problem of low counts in a signal plus noise model

Woodroofe, Michael ; Wang, Hsiuying

Ann. Statist., Tome 28 (2000) no. 3, p. 1561-1569 / Harvested from Project Euclid

Résumé

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.

Détail

Publié le : 2000-12-14
Classification:  Admissibility,  ancillary statistic,  Bayesian solutions,  confidence intervals,  neutrino oscillations,  $p$-values,  risk,  62C15,  62F03,  62P35