Abstract
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 EMalgorithm. Indeed, historically geneticists devised many special cases of the EM algorithm before it was generally formulated by Dempster et al. [5, 12]. 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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
2.9 References
Chakraborty R, Srinivasan MR, Daiger SP (1993) Evaluation of standard error and confidence interval of estimated multilocus genotype probabilities, and their applications in DNA forensics. Amer J Hum Genet 52:60–70
Clarke CA, Price-Evans DA, McConnell RB, Sheppard PM (1959) Secretion of blood group antigens and peptic ulcers. Brit Med J 1:603–607
Crow JF (1965) Problems of ascertainment in the analysis of family data. Epidemiology and Genetics of Chronic Disease. Public Health Service Publication 1163, Neel JV, Shaw MW, Schull WJ, editors, Department of Health, Education, and Welfare, Washington, DC
Crow JF (1986) Basic Concepts in Population, Quantitative, and Ecological Genetics. Freeman, San Francisco
Dempster AP, Laird NM, Rubin DB (1977) Maximum likelihood from incomplete data via the EM algorithm (with discussion). J Roy Stat Soc B 39:1–38
Ferguson TS (1996) A Course in Large Sample Theory. Chapman & Hall, London
Flury B, Zoppe A (2000) Exercises in EM. Amer Statistician 54:207–209
Lawrence CE, Reilly AA (1990) An expectation maximization (EM) algorithm for the identification and characterization of common sites in unaligned bipolymer sequences. Proteins 7:41–51
Little RJA, Rubin DB (1987) Statistical Analysis with Missing Data. Wiley, New York
Ott J (1977) Counting methods (EM algorithm) in human pedigree analysis: linkage and segregation analysis. Ann Hum Genet 40:443–454
Rao CR (1973) Linear Statistical Inference and Its Applications, 2nd ed. Wiley, New York
Smith CAB (1957) Counting methods in genetical statistics. Ann Hum Genet 21:254–276
Tanner MA (1993) Tools for Statistical Inference: Methods for the Exploration of Posterior Distributions and Likelihood Functions, 2nd ed. Springer-Verlag, New York
Thompson EA (1986) Pedigree Analysis in Human Genetics. Johns Hopkins University Press, Baltimore
Titterington DM, Smith AFM, Makov UE (1985) Statistical Analysis of Finite Mixture Distributions. Wiley, New York
Weeks DE, Lange K (1989) Trials, tribulations, and triumphs of the EM algorithm in pedigree analysis. IMA J Math Appl Med Biol 6:209–232
Weir BS (1996) Genetic Data Analysis II. Sinauer, Sunderland, MA
Rights and permissions
Copyright information
© 2003 Springer-Verlag New York, Inc.
About this chapter
Cite this chapter
(2003). Counting Methods and the EM Algorithm. In: Applied Probability. Springer Texts in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-0-387-22711-5_2
Download citation
DOI: https://doi.org/10.1007/978-0-387-22711-5_2
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-00425-9
Online ISBN: 978-0-387-22711-5
eBook Packages: Springer Book Archive