Probability functions on complex pedigrees
- 1 March 1978
- journal article
- research article
- Published by Cambridge University Press (CUP) in Advances in Applied Probability
- Vol. 10 (01) , 26-61
- https://doi.org/10.1017/s0001867800029475
Abstract
The calculation of probabilities on pedigrees of arbitrary complexity is discussed for a basic model of transmission and penetrance (encompassing Mendelian inheritance, and certain environmental influences). The structure of pedigrees, and the types of loops occurring, is discussed. Some results in graph theory are obtained and, using these, a recurrence relation derived for certain probabilities. The recursive procedure enables the successive peeling off of certain members of the pedigree, and the condensation of the information on those individuals into a function on a subset of those remaining. The underlying theory is set out, and examples given of the utilization of the resulting algorithm.Keywords
This publication has 8 references indexed in Scilit:
- The recursive derivation of likelihoods on complex pedigreesAdvances in Applied Probability, 1976
- Calculation of risk factors and likelihoods for familial diseasesComputers and Biomedical Research, 1976
- The use of matrices in calculating mendelian probabilitiesAnnals of Human Genetics, 1976
- Inference of genealogical structureSocial Science Information, 1976
- The estimation of pairwise relationshipsAnnals of Human Genetics, 1975
- Extensions to Pedigree AnalysisHuman Heredity, 1975
- A General Model for the Genetic Analysis of Pedigree DataHuman Heredity, 1971
- Segregation Analysis in Human GeneticsScience, 1958