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Estimation of Distribution Overlap of Urn Models
A classical problem in statistics is estimating the expected coverage of a sample, which has had applications in gene expression, microbial ecology, optimization, and even numismatics. Here we consider a related extension of this problem to random samples of two discrete distributions. Specifically,...
Autores principales: | , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Public Library of Science
2012
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3491072/ https://www.ncbi.nlm.nih.gov/pubmed/23139734 http://dx.doi.org/10.1371/journal.pone.0042368 |
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author | Hampton, Jerrad Lladser, Manuel E. |
author_facet | Hampton, Jerrad Lladser, Manuel E. |
author_sort | Hampton, Jerrad |
collection | PubMed |
description | A classical problem in statistics is estimating the expected coverage of a sample, which has had applications in gene expression, microbial ecology, optimization, and even numismatics. Here we consider a related extension of this problem to random samples of two discrete distributions. Specifically, we estimate what we call the dissimilarity probability of a sample, i.e., the probability of a draw from one distribution not being observed in [Image: see text] draws from another distribution. We show our estimator of dissimilarity to be a [Image: see text]-statistic and a uniformly minimum variance unbiased estimator of dissimilarity over the largest appropriate range of [Image: see text]. Furthermore, despite the non-Markovian nature of our estimator when applied sequentially over [Image: see text], we show it converges uniformly in probability to the dissimilarity parameter, and we present criteria when it is approximately normally distributed and admits a consistent jackknife estimator of its variance. As proof of concept, we analyze V35 16S rRNA data to discern between various microbial environments. Other potential applications concern any situation where dissimilarity of two discrete distributions may be of interest. For instance, in SELEX experiments, each urn could represent a random RNA pool and each draw a possible solution to a particular binding site problem over that pool. The dissimilarity of these pools is then related to the probability of finding binding site solutions in one pool that are absent in the other. |
format | Online Article Text |
id | pubmed-3491072 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2012 |
publisher | Public Library of Science |
record_format | MEDLINE/PubMed |
spelling | pubmed-34910722012-11-08 Estimation of Distribution Overlap of Urn Models Hampton, Jerrad Lladser, Manuel E. PLoS One Research Article A classical problem in statistics is estimating the expected coverage of a sample, which has had applications in gene expression, microbial ecology, optimization, and even numismatics. Here we consider a related extension of this problem to random samples of two discrete distributions. Specifically, we estimate what we call the dissimilarity probability of a sample, i.e., the probability of a draw from one distribution not being observed in [Image: see text] draws from another distribution. We show our estimator of dissimilarity to be a [Image: see text]-statistic and a uniformly minimum variance unbiased estimator of dissimilarity over the largest appropriate range of [Image: see text]. Furthermore, despite the non-Markovian nature of our estimator when applied sequentially over [Image: see text], we show it converges uniformly in probability to the dissimilarity parameter, and we present criteria when it is approximately normally distributed and admits a consistent jackknife estimator of its variance. As proof of concept, we analyze V35 16S rRNA data to discern between various microbial environments. Other potential applications concern any situation where dissimilarity of two discrete distributions may be of interest. For instance, in SELEX experiments, each urn could represent a random RNA pool and each draw a possible solution to a particular binding site problem over that pool. The dissimilarity of these pools is then related to the probability of finding binding site solutions in one pool that are absent in the other. Public Library of Science 2012-11-06 /pmc/articles/PMC3491072/ /pubmed/23139734 http://dx.doi.org/10.1371/journal.pone.0042368 Text en © 2012 Hampton, Lladser 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 Hampton, Jerrad Lladser, Manuel E. Estimation of Distribution Overlap of Urn Models |
title | Estimation of Distribution Overlap of Urn Models |
title_full | Estimation of Distribution Overlap of Urn Models |
title_fullStr | Estimation of Distribution Overlap of Urn Models |
title_full_unstemmed | Estimation of Distribution Overlap of Urn Models |
title_short | Estimation of Distribution Overlap of Urn Models |
title_sort | estimation of distribution overlap of urn models |
topic | Research Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3491072/ https://www.ncbi.nlm.nih.gov/pubmed/23139734 http://dx.doi.org/10.1371/journal.pone.0042368 |
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