Counting Methods and the EM Algorithm
In this chapter and the next, we undertake the study of estimation methods and their applications in genetics. Because of the complexity of genetic models, geneticists by and large rely on maximum likelihood estimators rather than on competing estimators derived from minimax, invariance, robustness, or Bayesian principles. A host of methods exists for numerically computing maximum likelihood estimates. Some of the most appealing involve simple counting arguments and the EM algorithm. Indeed, historically geneticists devised many special cases of the EM algorithm before it was generally formulated by Dempster et al. [5,9]. Our initial example retraces some of the steps in the long march from concrete problems to an abstract algorithm applicable to an astonishing variety of statistical models.
KeywordsSuccess Probability Affected Sibling Color Blindness Codominant Allele Complete Data Likelihood
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