Abstract
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.
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References
Blank, T. (1990) The MasPar MP-1 Architecture. Proceedings of IEEE CompCon, IEEE.
Cannings, C., Thompson, E. A. and Skolnick, M. H. (1978) Probability functions on complex pedigrees. Advances in Applied Probability, 10, 26–61.
Elston, R. C. and Stewart, J. (1971) A general model for the genetic analysis of pedigree data. Human Heredity, 21, 523–42.
Geman, S. and Geman, D. (1984) Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. IEEE Transactions on Pattern Analysis and Machine Intelligence, 45, 721–41.
Geyer, C. J. (1991) Markov chain Monte Carlo maximum likelihood for dependent data. In Computer Science and Statistics; 23rd Symposium on the Interface.
Kernighan, B. W. and Ritchie, D. M. (1978) The C Programming Language. Prentice-Hall, Englewood Cliffs, NJ.
Lauritzen, S. L. and Spiegelhalter, D. J. (1988) Local computations with probabilities on graphical structures and their applications to expert systems. Journal of the Royal Statistical Society, Series B, 50, 157–224.
Lewis, H. E. (1963) The Tristan islanders: a medical study of isolation. New Scientist, 20, 720–2.
Lin, S. (1992) On the performance of Markov chain Monte Carlo methods on pedigree data and a new algorithm, Technical Report 231, Department of Statistics, University of Washington, Seattle, Washington, USA.
Lin, S., Thompson, E. and Wijsman, E. (1993) Achieving irreducibility of the Markov chain Monte Carlo method applied to pedigree data. IMA Journal of Mathematics Applied in Medicine and Biology, 10, 1–17.
MP1 (1990) MP-1 Standard Programming Manuals, Language Reference.
Roberts, D. F. (1967) The development of inbreeding in an island population. Ciencia e Cultura, 19, 78–84.
Roberts, D. F. (1968) Genetic effects of population size reduction. Nature, 220, 1084–8.
Roberts, D. F. (1971) The demography of Tristan da Cunha. Population Studies, 25, 469–75.
Sheehan, N. (1990) Genetic Restoration on Complex Pedigrees, PhD thesis, University of Washington.
Sheehan, N. and Thomas, A. (1993) On the irreducibility of a Markov chain defined on a space of genotype configurations by a sampling scheme. Biometrics, 49, 163–75.
Thomas, A. (1985) Data structures, methods of approximation and optimal computation for pedigree analysis. PhD thesis, Cambridge University.
Thomas, A. (1986) Approximate computation of probability functions for pedigree analysis. IMA Journal of Mathematics Applied in Medicine and Biology, 3, 157–66.
Thomas, A. (1993) A note on the four-colourability of pedigrees and its consequences for probability calculations. Statistics and Computing, 3, 51–4.
Thompson, E. A. (1978) Ancestral inference II, the founders of Tristan da Cunha. Annals of Human Genetics, 42, 239–53.
Wright, Z. L. (1991) Ancestral inference by simulation: the ABO blood types on Tristan da Cunha, Master's thesis, University of Bath.
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Bradford, R., Thomas, A. Markov chain Monte Carlo methods for family trees using a parallel processor. Stat Comput 6, 67–75 (1996). https://doi.org/10.1007/BF00161575
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DOI: https://doi.org/10.1007/BF00161575