The problem of low counts in a signal plus noise model

Michael Woodroofe*, Hsiuying Wang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


Consider the model X = B + S, where B and S are independent Poisson random variables with means μ and ν, ν is unknown, but μ 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 ≤ 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.

Original languageEnglish
Pages (from-to)1561-1569
Number of pages9
JournalAnnals of Statistics
Issue number6
StatePublished - 1 Dec 2000


  • Admissibility
  • Ancillary statistic
  • Bayesian solutions
  • Confidence intervals
  • Neutrino oscillations
  • Risk
  • p-values


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