A Justification of a Negative Binomial Model For Target Sightings
Author: McCue, Brian
Source: Military Operations Research, Volume 8, Number 4, 2003 , pp. 33-41(9)
Publisher: Military Operations Research Society
Abstract:A long-standing formal proof shows that if the mean of a Poisson distribution is itself gamma-distributed then the resulting compound distribution is the negative-binomial. This fact is sometimes used in the context of searches, in which the unknown true mean of the Poisson-distributed number of sightings is replaced by a gamma-distributed variable mean. This paper presents a heuristic path to the negative binomial distributed sightings, without the assumption of the gamma-distributed mean. Then the gamma distribution is recovered, as the result of the Bayesian updating of a reciprocal, or Jeffreys, prior distribution for the mean with one or more Poisson-distributed sighting counts.
Keywords: Application Areas: Campaign Analysis; Application Areas: Measures of Effectiveness; Application Areas: Operations Research and Intelligence; OR Methodologies: Bayesian Updating; OR Methodologies: Probabilistic Operations Research; OR Methodologies: Search Theory and Applied Statistics
Document Type: Research Article
Publication date: 2003
- Military Operations Research is the leading peer-reviewed journal publishing articles in the fields that describe operations research (OR) methodologies and theories used in key military applications.
MOR specifically invites papers that are significant military OR applications. Of particular interest are papers that present case studies showing innovative OR applications, apply OR to major policy issues, introduce interesting new problem areas, highlight educational issues, and document the history of military OR.
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