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Reference Priors for Poisson Processes Involving Nuisance Parameters

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  • Dieter Grientschnig

Abstract

A Bayesian reference analysis for determining the posterior distribution of the strength of a radiation source is performed. The only pieces of information available are the numbers of counts gathered in a gross and a background measurement along with the respective counting times and a state-of-knowledge distribution for the efficiency. This situation is addressed by combining the calculations of a “one-at-a-time” reference prior and a reference prior with partial information. The posterior distribution of the source strength obtained with the reference prior leads to credible intervals that have better frequentist coverage than corresponding intervals founded on uniform or Jeffreys’ priors.

Suggested Citation

  • Dieter Grientschnig, 2015. "Reference Priors for Poisson Processes Involving Nuisance Parameters," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(23), pages 4893-4911, December.
    • Handle: RePEc:taf:lstaxx:v:44:y:2015:i:23:p:4893-4911
    DOI: 10.1080/03610926.2013.800880
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