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Bayesian inference for disease prevalence using negative binomial group testing
Author(s) -
Pritchard Nicholas A.,
Tebbs Joshua M.
Publication year - 2011
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.201000148
Subject(s) - statistics , negative binomial distribution , bayesian probability , mathematics , estimator , point estimation , confidence interval , bayesian inference , binomial distribution , inference , sampling (signal processing) , posterior probability , inverse probability , econometrics , computer science , poisson distribution , artificial intelligence , filter (signal processing) , computer vision
Group testing, also known as pooled testing, and inverse sampling are both widely used methods of data collection when the goal is to estimate a small proportion. Taking a Bayesian approach, we consider the new problem of estimating disease prevalence from group testing when inverse (negative binomial) sampling is used. Using different distributions to incorporate prior knowledge of disease incidence and different loss functions, we derive closed form expressions for posterior distributions and resulting point and credible interval estimators. We then evaluate our new estimators, on Bayesian and classical grounds, and apply our methods to a West Nile Virus data set.