Reconstruction of Probability Distributions in Population Genetics

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dc.contributor.advisor Fewster, R en
dc.contributor.advisor Wang, Y en
dc.contributor.author Liu, Jing en
dc.date.accessioned 2012-08-05T19:58:23Z en
dc.date.issued 2012 en
dc.identifier.uri http://hdl.handle.net/2292/19403 en
dc.description.abstract For a range of models in population genetics, we demonstrate that moments of the stationary distribution can be obtained without knowing the stationary distribution itself, using the diffusion approximation. We introduce the maximum entropy principle to use these acquired moments to reconstruct the density of the stationary distribution. This procedure is illustrated by reconstructing the stationary distribution for a two-locus model with linkage and recurrent mutation. Using the reconstructed stationary distribution, the mean and the variance of a linkage disequilibrium measure r² are evaluated for the model. We then propose a novel method for reconstructing unknown distributions analytically based on the maximum entropy principle. Given a sequence of moments expressed in terms of the underlying population parameter, this new method offers a likelihood function for parameter estimation by expressing the density of observable quantities as an explicit function of the data and the parameter. en
dc.publisher ResearchSpace@Auckland en
dc.relation.ispartof PhD Thesis - University of Auckland en
dc.rights Items in ResearchSpace are protected by copyright, with all rights reserved, unless otherwise indicated. Previously published items are made available in accordance with the copyright policy of the publisher. en
dc.rights.uri https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm en
dc.rights.uri http://creativecommons.org/licenses/by-nc-sa/3.0/nz/ en
dc.title Reconstruction of Probability Distributions in Population Genetics en
dc.type Thesis en
thesis.degree.grantor The University of Auckland en
thesis.degree.level Doctoral en
thesis.degree.name PhD en
dc.rights.holder Copyright: The author en
dc.rights.accessrights http://purl.org/eprint/accessRights/OpenAccess en
pubs.elements-id 359219 en
pubs.org-id Science en
pubs.org-id Statistics en
pubs.record-created-at-source-date 2012-08-06 en


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http://creativecommons.org/licenses/by-nc-sa/3.0/nz/ Except where otherwise noted, this item's license is described as http://creativecommons.org/licenses/by-nc-sa/3.0/nz/

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