Trials, Tribulations, and Triumphs of the EM Algorithm in Pedigree Analysis
D.E. Weeks, K. Lange
IMA Journal of Mathematics Applied in Medicine & Biology,
6(4), 209-232 (1989)
Abstract
The EM algorithm is an iterative method for finding
maximum-likelihood estimates. Its advantages often include numerical
stability, simplicity of computer implementation, and natural
incorporation of parameter constraints. However, the EM algorithm
must be tailored to each specific problem. Smith (1957) and Ott
(1977, 1979) have accomplished this for a variety of problems in
human pedigree analysis. The present paper clarifies their theory by
presenting it from a modern perspective. Five practical numerical
examples are also given in an attempt to assess the value of the EM
algorithm in realistic genetic modelling. These examples deal with
racial admixture, linkage homogeneity, classical segregation
analysis, a Mendelian latent trait model for schizophrenia, and a
heterozygote detection assay for Ataxia-telangiectasia. Comparison
with a quasi-Newton method of optimization reveals that the EM
algorithm generally converges more slowly, but also more stably.
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