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Bayesian Inference from Count Data Using Discrete Uniform Priors
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-c...
Autores principales: | , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Public Library of Science
2013
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3792115/ https://www.ncbi.nlm.nih.gov/pubmed/24116003 http://dx.doi.org/10.1371/journal.pone.0074388 |
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author | Comoglio, Federico Fracchia, Letizia Rinaldi, Maurizio |
author_facet | Comoglio, Federico Fracchia, Letizia Rinaldi, Maurizio |
author_sort | Comoglio, Federico |
collection | PubMed |
description | 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. |
format | Online Article Text |
id | pubmed-3792115 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2013 |
publisher | Public Library of Science |
record_format | MEDLINE/PubMed |
spelling | pubmed-37921152013-10-10 Bayesian Inference from Count Data Using Discrete Uniform Priors Comoglio, Federico Fracchia, Letizia Rinaldi, Maurizio PLoS One Research Article 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. Public Library of Science 2013-10-07 /pmc/articles/PMC3792115/ /pubmed/24116003 http://dx.doi.org/10.1371/journal.pone.0074388 Text en © 2013 Comoglio et al http://creativecommons.org/licenses/by/4.0/ This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are properly credited. |
spellingShingle | Research Article Comoglio, Federico Fracchia, Letizia Rinaldi, Maurizio Bayesian Inference from Count Data Using Discrete Uniform Priors |
title | Bayesian Inference from Count Data Using Discrete Uniform Priors |
title_full | Bayesian Inference from Count Data Using Discrete Uniform Priors |
title_fullStr | Bayesian Inference from Count Data Using Discrete Uniform Priors |
title_full_unstemmed | Bayesian Inference from Count Data Using Discrete Uniform Priors |
title_short | Bayesian Inference from Count Data Using Discrete Uniform Priors |
title_sort | bayesian inference from count data using discrete uniform priors |
topic | Research Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3792115/ https://www.ncbi.nlm.nih.gov/pubmed/24116003 http://dx.doi.org/10.1371/journal.pone.0074388 |
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