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The maximum of a function of a Markov chain and application to linkage analysis

Part of: Stochastic processes

Published online by Cambridge University Press:  01 July 2016

I-Ping Tu  and
David Siegmund
I-Ping Tu*
Affiliation:
Stanford University
David Siegmund*
Affiliation:
Stanford University
*
∗ Postal address: Department of Health Research and Policy, Stanford University, Stanford, CA 94305, USA.
∗∗ Postal address: Department of Statistics, Stanford University, 390 Serra Mall, Stanford, CA 94305-4065, USA. Email address: dos@stat.stanford.edu
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Abstract

One method of linkage analysis in humans is based on identity-by-descent of pairs of relatives who share a phenotype of interest (for example, a particular disease). We replace the convenient assumption of continuous specification of regions of identity by descent by the more realistic, although still artificially simple, assumption of data from a discrete set of equally spaced infinitely polymorphic markers. We generalize the continuous time Markov chain analysis of Feingold (1993b) and compare the accuracy of the new approximation with that of the simpler Gaussian approximation of Feingold, Brown and Siegmund (1993) under a variety of assumptions about the composition of the pedigrees to be studied. We also suggest a perturbation of the Gaussian approximation as a compromise to achieve reasonable accuracy with minimal computational effort.

Keywords

Markov chaingene mappinggenome scan

MSC classification

Primary: 60G55: Point processes
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 31 , Issue 2 , June 1999 , pp. 510 - 531
Copyright
Copyright © Applied Probability Trust 1999 

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