Applications of the Dirichlet distribution to forensic match probabilities

  • Kenneth Lange
Part of the Contemporary Issues in Genetics and Evolution book series (CIGE, volume 4)


The Dirichlet distribution provides a convenient conjugate prior for Bayesian analyses involving multinomial proportions. In particular, allele frequency estimation can be carried out with a Dirichlet prior. If data from several distinct populations are available, then the parameters characterizing the Dirichlet prior can be estimated by maximum likelihood and then used for allele frequency estimation in each of the separate populations. This empirical Bayes procedure tends to moderate extreme multinomial estimates based on sample proportions. The Dirichlet distribution can also be employed to model the contributions from different ancestral populations in computing forensic match probabilities. If the ancestral populations are in genetic equilibrium, then the product rule for computing match probabilities is valid conditional on the ancestral contributions to a typical person of the reference population. This fact facilitates computation of match probabilities and tight upper bounds to match probabilities.

Key words

genetic equilibrium racial admixture Monte Carlo upper bounds 


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Copyright information

© Springer Science+Business Media Dordrecht 1995

Authors and Affiliations

  • Kenneth Lange
    • 1
  1. 1.Department of Biostatistics, School of Public HealthUniversity of MichiganAnn ArborUSA

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