Markov chain Monte Carlo methods for family trees using a parallel processor

A 1024 CPU parallel computer is used to obtain simulated genotypes in the Tristan da Cunha pedigree using random local updating methods. A four-colour theorem is invoked to justify simultaneous updating. Multiple copies of the program are run simultaneously. These results are used to infer the source of the B allele of the ABO blood group that is present in the population.

[1]  E A Thompson,et al.  Ancestral inference , 1978, Annals of human genetics.

[2]  Elizabeth A. Thompson,et al.  Genetic restoration on complex pedigrees , 1990 .

[3]  Alun Thomas,et al.  A note on the four-colourability of pedigrees and its consequences for probability calculations , 1993 .

[4]  Bjarne Stroustrup,et al.  C++ Programming Language , 1986, IEEE Softw..

[5]  Probability functions on complex pedigrees , 1978 .

[6]  R. Elston,et al.  A general model for the genetic analysis of pedigree data. , 1971, Human heredity.

[7]  David J. Spiegelhalter,et al.  Local computations with probabilities on graphical structures and their application to expert systems , 1990 .

[8]  E. Wijsman,et al.  Achieving irreducibility of the Markov chain Monte Carlo method applied to pedigree data. , 1993, IMA journal of mathematics applied in medicine and biology.

[9]  D. F. Roberts,et al.  The demography of Tristan da Cunha. , 1971, Population studies.

[10]  A. Thomas Approximate computation of probability functions for pedigree analysis. , 1986, IMA journal of mathematics applied in medicine and biology.

[11]  N. Sheehan,et al.  On the irreducibility of a Markov chain defined on a space of genotype configurations by a sampling scheme. , 1993, Biometrics.

[12]  Shili Lin,et al.  ON THE PERFORMANCE OF MARKOV CHAIN MONTE CARLO METHODS ON PEDIGREE DATA AND A NEW ALGORITHM , 1992 .

[13]  C. Geyer Markov Chain Monte Carlo Maximum Likelihood , 1991 .

[14]  Donald Geman,et al.  Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[15]  D. F. Roberts,et al.  Genetic Effects of Population Size Reduction , 1968, Nature.

[16]  Tom Blank,et al.  The MasPar MP-1 architecture , 1990, Digest of Papers Compcon Spring '90. Thirty-Fifth IEEE Computer Society International Conference on Intellectual Leverage.