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Bayesian Inference from Count Data Using Discrete Uniform Priors

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  • Federico Comoglio
  • Letizia Fracchia
  • Maurizio Rinaldi

Abstract

We consider a set of sample counts obtained by sampling arbitrary fractions of a finite volume containing an homogeneously dispersed population of identical objects. We report a Bayesian derivation of the posterior probability distribution of the population size using a binomial likelihood and non-conjugate, discrete uniform priors under sampling with or without replacement. Our derivation yields a computationally feasible formula that can prove useful in a variety of statistical problems involving absolute quantification under uncertainty. We implemented our algorithm in the R package dupiR and compared it with a previously proposed Bayesian method based on a Gamma prior. As a showcase, we demonstrate that our inference framework can be used to estimate bacterial survival curves from measurements characterized by extremely low or zero counts and rather high sampling fractions. All in all, we provide a versatile, general purpose algorithm to infer population sizes from count data, which can find application in a broad spectrum of biological and physical problems.

Suggested Citation

  • Federico Comoglio & Letizia Fracchia & Maurizio Rinaldi, 2013. "Bayesian Inference from Count Data Using Discrete Uniform Priors," PLOS ONE, Public Library of Science, vol. 8(10), pages 1-8, October.
    • Handle: RePEc:plo:pone00:0074388
    DOI: 10.1371/journal.pone.0074388
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    References listed on IDEAS

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    1. Satoshi Morita & Peter F. Thall & Peter Müller, 2008. "Determining the Effective Sample Size of a Parametric Prior," Biometrics, The International Biometric Society, vol. 64(2), pages 595-602, June.
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