Parameter Estimation for the Dirichlet-Multinomial Distribution

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PetersonMath627.pdf (456.89 KB)

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https://userpages.umbc.edu/~gobbert/papers/PetersonMath627.pdf

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http://hdl.handle.net/11603/11687

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UMBC Mathematics and Statistics Department

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2011-05-20

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technical report
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Subjects

Parallel Computing
Fisher Scoring Algorithm
Maximum Likelihood Estimation
Dirichlet-Multinomial
UMBC High Performance Computing Facility (HPCF)

Abstract

In the 1998 paper entitled Large Cluster Results for Two Parametric Multinomial Extra Variation Models, Nagaraj K. Neerchal and Jorge G. Morel developed an approximation to the Fisher information matrix used in the Fisher Scoring algorithm for finding the maximum likelihood estimates of the parameters of the Dirichlet-multinomial distribution. They performed simulation studies comparing the results of the approximation to the results of the usual Fisher Scoring algorithm, for varying dimensions of the parameter vector. In this study, parallel computing in R is utilized to extend the previous simulation studies to larger dimensions. Additionally, the Fisher Scoring algorithm and the direct numerical maximization of the maximum likelihood are compared.