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The use of matrices in calculating mendelian probabilities

The use of matrices in calculating mendelian probabilities BY CEDRIC A . B . SMITH Galton Laboratory, University College London, Cower Street, London, KC. 1 Bolling, Chase & Murphy (1976) have shown that the calculation of genetic probabilities for counselling can be put into a neat systematic form by the use of matrices. I n the following paper I attempt to spell their method out more explicitly and in detail. No great originality is claimed for this, since most of the ideas involved will be found either explicitly stated or implied in the paper by Bolling et al. But it may be useful to have the formulas in a more general form than they give, enabling them to be used with more complicated genetic systems. The mathematical formulation brings out more clearly the relations between probability and likelihood in statistical inference. An alternative method of calculating mendelian probabilities is provided by Hilden’s (1970) ‘Genstat ’. This concentrates on expressing and manipulating probabilities in terms of generating functions. It provides a powerful approach, but suitable for dealing with joint distributions. I n the method of Bolling et al. as developed here, the purpose is rather to f k d the probabilities for a single individual in a http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Annals of Human Genetics Wiley

The use of matrices in calculating mendelian probabilities

SMITH, CEDRIC A. B.
Annals of Human Genetics , Volume 40 (1) – Jul 1, 1976
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References (16)

Publisher
Wiley
Copyright
Copyright © 1976 Wiley Subscription Services, Inc., A Wiley Company
ISSN
0003-4800
eISSN
1469-1809
DOI
10.1111/j.1469-1809.1976.tb00163.x
Publisher site
See Article on Publisher Site

Abstract

BY CEDRIC A . B . SMITH Galton Laboratory, University College London, Cower Street, London, KC. 1 Bolling, Chase & Murphy (1976) have shown that the calculation of genetic probabilities for counselling can be put into a neat systematic form by the use of matrices. I n the following paper I attempt to spell their method out more explicitly and in detail. No great originality is claimed for this, since most of the ideas involved will be found either explicitly stated or implied in the paper by Bolling et al. But it may be useful to have the formulas in a more general form than they give, enabling them to be used with more complicated genetic systems. The mathematical formulation brings out more clearly the relations between probability and likelihood in statistical inference. An alternative method of calculating mendelian probabilities is provided by Hilden’s (1970) ‘Genstat ’. This concentrates on expressing and manipulating probabilities in terms of generating functions. It provides a powerful approach, but suitable for dealing with joint distributions. I n the method of Bolling et al. as developed here, the purpose is rather to f k d the probabilities for a single individual in a

Journal

Annals of Human Genetics – Wiley

Published: Jul 1, 1976

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