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A hierarchical Bayesian approach for estimating the origin of a mixed population

Feng Guo, Dipak K. Dey, and Kent E. Holsinger

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Abstract

We propose a hierarchical Bayesian model to estimate the proportional contribution of source populations to a newly founded colony. Samples are derived from the first generation offspring in the colony, but mating may occur preferentially among migrants from the same source population. Genotypes of the newly founded colony and source populations are used to estimate the mixture proportions, and the mixture proportions are related to environmental and demographic factors that might affect the colonizing process. We estimate an assortative mating coefficient, mixture proportions, and regression relationships between environmental factors and the mixture proportions in a single hierarchical model. The first-stage likelihood for genotypes in the newly founded colony is a mixture multinomial distribution reflecting the colonizing process. The environmental and demographic data are incorporated into the model through a hierarchical prior structure. A simulation study is conducted to investigate the performance of the model by using different levels of population divergence and number of genetic markers included in the analysis. We use Markov chain Monte Carlo (MCMC) simulation to conduct inference for the posterior distributions of model parameters. We apply the model to a data set derived from grey seals in the Orkney Islands, Scotland. We compare our model with a similar model previously used to analyze these data. The results from both the simulation and application to real data indicate that our model provides better estimates for the covariate effects.

Chapter information

Source
Bertrand Clarke and Subhashis Ghosal, eds., Pushing the Limits of Contemporary Statistics: Contributions in Honor of Jayanta K. Ghosh (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2008), 237-250

Dates
First available in Project Euclid: 28 April 2008

Permanent link to this document
https://projecteuclid.org/euclid.imsc/1209398472

Digital Object Identifier
doi:10.1214/074921708000000174

Mathematical Reviews number (MathSciNet)
MR2459228

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]

Keywords
hierarchical Bayes MCMC multinomial

Rights
Copyright © 2008, Institute of Mathematical Statistics

Citation

Guo, Feng; Dey, Dipak K.; Holsinger, Kent E. A hierarchical Bayesian approach for estimating the origin of a mixed population. Pushing the Limits of Contemporary Statistics: Contributions in Honor of Jayanta K. Ghosh, 237--250, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2008. doi:10.1214/074921708000000174. https://projecteuclid.org/euclid.imsc/1209398472


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