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Markov processes for modeling and analyzing a new genetic mapping method

Part of: Markov processes

Published online by Cambridge University Press:  14 July 2016

Eleanor Feingold
Eleanor Feingold*
Affiliation:
Stanford University
*
∗ Present address: Division of Biostatistics, Emory University School of Public Health, 1599 Clifton Road NE, Atlanta, GA 30329, USA.
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Abstract

This paper describes a set of stochastic processes that is useful for modeling and analyzing a new genetic mapping method. Some of the processes are Markov chains, and some are best described as functions of Markov chains. The central issue is boundary-crossing probabilities, which correspond to p-values for the existence of genes for particular traits. The methods elaborated by Aldous (1989) provide very accurate approximate p-values, as spot-checked against simulations.

Keywords

MARKOV CHAINBOUNDARY-CROSSING PROBABILITYPOISSON APPROXIMATION

MSC classification

Primary: 60J27: Continuous-time Markov processes on discrete state spaces
Secondary: 92D10: Genetics
Type
Research Papers
Information
Journal of Applied Probability , Volume 30 , Issue 4 , December 1993 , pp. 766 - 779
Copyright
Copyright © Applied Probability Trust 1993 

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References

Aldous, D. (1989) Probability Approximations via the Poisson Clumping Heuristic. Springer-Verlag, New York.CrossRefGoogle Scholar
Gonick, L. and Wheelis, M. (1989) The Cartoon Guide to Genetics. Harper and Row, New York.Google Scholar
Keilson, J. (1979) Markov Chain Models - Rarity and Exponentiality . Springer-Verlag, New York.Google Scholar
Ott, J. (1985) Analysis of Human Genetic Linkage. Johns Hopkins University Press, Baltimore.Google Scholar
Lander, E. S. and Botstein, D. (1989) Mapping mendelian factors underlying quantitative traits using RFLP linkage maps. Genetics 121, 185–199.Google Scholar
Leadbetter, M. R., Lindgren, G. and Rootzen, H. (1983) Extremes and Related Properties of Random Sequences and Processes. Springer-Verlag, New York.Google Scholar
Risch, N. (1990) Linkage strategies for genetically complex traits. II. The power of affected relative pairs. Amer. J. Hum. Genet. 46, 226–241.Google Scholar
Thompson, E.A. (1986) Pedigree Analysis in Human Genetics. Johns Hopkins University Press, Baltimore.Google Scholar
Feingold, E. (1993) Modeling a New Genetic Mapping. Ph.D. Dissertation, Stanford University.Google Scholar
Feingold, E., Brown, P. O. and Siegmund, D. (1993) Gaussian models for genetic linkage analysis using complete high-resolution maps of identity by descent. Amer. J. Hum. Genet. 53, 234–251.Google Scholar
Nelson, S. F. et al. (1993) Genomic mismatch scanning: a new approach to genetic linkage mapping. Nature Genetics 4, 11–18.Google Scholar