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Bayesian interval estimation for the difference of two independent Poisson rates using data subject to under‐reporting
Author(s) -
Greer Brandi A.,
Stamey James D.,
Young Dean M.
Publication year - 2011
Publication title -
statistica neerlandica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.52
H-Index - 39
eISSN - 1467-9574
pISSN - 0039-0402
DOI - 10.1111/j.1467-9574.2011.00483.x
Subject(s) - poisson distribution , prior probability , identifiability , statistics , bayesian probability , interval estimation , interval (graph theory) , count data , credible interval , econometrics , estimator , mathematics , poisson regression , confidence interval , computer science , medicine , population , environmental health , combinatorics
Comparing occurrence rates of events of interest in science, business, and medicine is an important topic. Because count data are often under‐reported, we desire to account for this error in the response when constructing interval estimators. In this article, we derive a Bayesian interval for the difference of two Poisson rates when counts are potentially under‐reported. The under‐reporting causes a lack of identifiability. Here, we use informative priors to construct a credible interval for the difference of two Poisson rate parameters with under‐reported data. We demonstrate the efficacy of our new interval estimates using a real data example. We also investigate the performance of our newly derived Bayesian approach via simulation and examine the impact of various informative priors on the new interval.