Finding noncommunicating sets for Markov chain Monte Carlo estimations on pedigrees

Journal Article · Fri Apr 01 04:00:00 EST 1994 · American Journal of Human Genetics; (United States)

OSTI ID:7105174

Lin, S ^[1]; Thompson, E; Wijsman, E ^[2]

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1. Univ. of California, Berkeley, CA (United States)
2. Univ. of Washington, Seattle, WA (United States)

Markov chain Monte Carlo (MCMC) has recently gained use as a method of estimating required probability and likelihood functions in pedigree analysis, when exact computation is impractical. However, when a multiallelic locus is involved, irreducibility of the constructed Markov chain, an essential requirement of the MCMC method, may fail. Solutions proposed by several researchers, which do not identify all the noncommunicating sets of genotypic configurations, are inefficient with highly polymorphic loci. This is a particularly serious problem in linkage analysis, because highly polymorphic markers are much more informative and thus are preferred. In the present paper, the authors describe an algorithm that finds all the noncommunicating classes of genotypic configurations on any pedigree. This leads to a more efficient method of defining an irreducible Markov chain. Examples, including a pedigree from a genetic study of familial Alzheimer disease, are used to illustrate how the algorithm works and how penetrances are modified for specific individuals to ensure irreducibility. 20 refs., 7 figs., 6 tabs.

• OSTI ID: 7105174
• Journal Information: American Journal of Human Genetics; (United States), Journal Name: American Journal of Human Genetics; (United States) Vol. 54:4; ISSN AJHGAG; ISSN 0002-9297
• Country of Publication: United States
• Language: English

Related Subjects

550400* -- Genetics
59 BASIC BIOLOGICAL SCIENCES
99 GENERAL AND MISCELLANEOUS
990200 -- Mathematics & Computers
CALCULATION METHODS
GENETIC MAPPING
MAPPING
MARKOV PROCESS
MATHEMATICS
MONTE CARLO METHOD
STATISTICS
STOCHASTIC PROCESSES