Multilocus linkage analysis by blocked Gibbs sampling

Statistics and Computing

Volumn 10, Issue 3, 2000, Pages 259-269

  Thomas, Alun ^a,b   Gutin, Alexander ^a   Abkevich, Victor ^a   Bansal, Aruna ^b,c  

^a Myriad Genetic Laboratories   (United States)

^b U of UT   (United States)

^c Genetic Research   (United States)

Author keywords

Genetic linkage; Graphical models; Markov chain Monte Carlo; Peeling

Indexed keywords

EID: 0042226484     PISSN: 09603174     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1008947712763     Document Type: Article

References (41)

1. Andersen S.K., Olesen K.G., Jensen F.V., and Jensen F. 1989. HUGIN-A shell for building belief universes for expert systems. In: Proceedings of the 11th International Joint Conference on Artificial Intelligence, pp. 1080-1085.
2. Cannings C., Thompson E.A., and Skolnick M.H. 1978. Probability functions on complex pedigrees. Annals of Applied Probability 10:26-61.
3. Cottingham R.W., Idury R.M., and Schaffer A.A. 1993. Faster sequential genetic linkage computations. American Journal of Human Genetics 53: 252-263.
4. Dawid A.P. 1992. Applications of a general propogation algorithm for probabilistic expert systems. Statistics and Computing 2: 25-36.
5. Dempster A.P., Laird N.M., and Rubin D.B. 1977. Maximum likelihood estimation from incomplete data via the EM algorithm (with discussion). Journal of the Royal Statistical Society, Series B 39: 1-38.
6. Elston R.C. and Stewart J. 1971. A general model for the genetic analysis of pedigree data. Human Heredity 21: 523-542.
7. Fischer L.P. 1990. Reference manual for the HUGIN Application Programming Interface. Technical Report, Hugin Expert A/S.
8. Gelfand A.E. and Smith A.F.M. 1990. Sampling-based approaches to calculating marginal densities. Journal of the American Statistical Association 85(410): 398-409.
9. Gelman A. and Rubin D.B. 1992. Inference from iterative simulation using single and multiple sequences (with discussion) 7: 457-511.
10. 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: 721-741.
11. Geyer C.J. 1992. Practical Markov chain Monte Carlo. Statistical Science 7: 156-163.
12. Harbron C. and Thomas A. 1994. Alternative graphical representations of genotypes in a pedigree. IMA Journal of Mathematics Applied in Medicine and Biology 11: 217-228.
13. Heath S.C. 1998. Generating consistent genotypic configurations for multi-allelic loci and large complex pedigrees. Human Heredity 48: 1-11.
14. Jensen C.S. 1997. Blocking Gibbs sampling for inference in large and complex Bayesian networks with applications in genetics. PhD Thesis, Department of Computer Science, Institute for Electronic Systems, Aalborg University, Denmark.
15. Jensen C.S. 1998. A simple method for finding a legal configuration in complex bayesian networks. Statistics and Computing 8(3): 243-251.
16. Jensen C.S. and Kong A. 1996. Blocking Gibbs sampling for linkage analysis in large pedigrees with many loops. Technical Report R-96-2048, Department of Computer Science, Aalborg University.
17. Jensen C.S., Kong A., and Kjaerulff U. 1995. Blocking-Gibbs sampling in very large probabilistic expert systems. International Journal of Human-Computer Studies 42: 647-666.
18. Jensen F.V. 1988. Local computation with probabilities on graphical structures and their application to expert systems, discussion contribution. Journal of the Royal Statistical Society, Series B 50: 157-224.
19. Jensen F.V. 1996. An Introduction to Bayesian Networks. UCL Press.
20. Kong A. 1991. Efficient methods for computing likage likelihoods of recessive diseases in inbred pedigrees. Genetic Epidemiology 8: 81-103.
21. Kong A., Cox N., Frigge M., and Irwin M. 1993. Sequential imputation and multipoint linkage analysis. Genetic Epidemiology 10: 483-488.
22. Kruglyak E., Daly M.J., Reeve-Daly M.P., and Eander E.S. 1996. Parametric and non-parametric linage analysis: A unified multipoint approach. American Journal of Human Genetics 58: 1347-1363.
23. Kruglyak E. and Lander E.S. 1998. Faster mulitipoint lankage analysis using Fourier transforms. Journal of Computational Biology 5(1): 1-7.
24. Lander E.S. and Green P. 1987. Construction of multilocus genetic maps in humans. Proc. Natl. Aca. Sci. USA 84: 2363-2367.
25. Lange K. and Elston R.C. 1975. Extensions to pedigree analysis. I. Likelihood calculations for simple and complex pedigrees. Human Heredity 25: 95-105.
26. Lathrop G.M., Lalouel J.M., Julier C., and Ott J. 1984. Strategies for multilocus linkage analysis in humans. Proc. Natl. Acad. Sci. USA 81: 3443-3446.
27. Lauritzen S.L. 1996. Graphical Models. Clarendon Press.
28. 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.
29. Morton N.B. 1955. Sequential tests for the detection of linkage. American Journal of Human Genetics 7: 23-30.
30. O'Connell J.R. and Weeks D.E. 1995. The VITESSE algorithm forrapid exact multilocus linkage analysis via genotype set-recoding and fuzzy inheritance. Nature Genetics 11: 402-408.
31. Ott J. 1989. Computer simulation methods in human linkage analysis. Proc. Natl. Acad. Sci. USA 86, 4175-4178.
32. Ploughman L.M. and Boehnke M. 1989. Estimating the power of a proposed linkage study for a complex genetic trait. American Journal of Human Genetics 44: 543-551.
33. Sheehan N. 1990. Genetic restoration on complex pedigrees. Ph.D. Thesis, University of Washington.
34. Sheehan N. 1992. Sampling genotypes on complex pedigrees with phenotypic constraints: The origin of the B allele among the Polar Eskimos. IMA Journal of Mathematics Applied in Medicine and Biology 9: 1-18.
35. 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: 163-175.
36. Smith A.F.M. and Roberts G.O. 1993. Bayesian computation via the Gibbs sampler and related Markov chain Monte Carlo methods. Journal of the Royal Statistical Society, Series B 55(1): 5-23.
37. Sobel E. and Lange K. 1996. Descent graphs in pedigree analysis: Applications to haplotyping, location scores, and marker-sharing statistics. American Journal of Human Genetics 58: 1323-1337.
38. Thomas A. 1986. Optimal computation of probability functions for pedigree analysis. IMA Journal of Mathematics Applied in Medicine and Biology 3: 167-178.
39. Thomas A. 1994. Linkage analysis on complex pedigrees by simulation. IMA Journal of Mathematics Applied in Medicine and Biology 11: 79-93.
40. Thomas A., Spiegelhalter D.J., and Gilks W.R. 1992. BUGS: A program to perform Bayesian inference using Gibbs sampling. In: Bernardo J.M., Berger J.O., Dawid A.P., and Smith A.F.M. (Eds.), Bayesian Statistics, Vol. 4. Oxford, Clarendon Press, pp. 837-842.
41. Whittemore A.S. and Halpern J. 1994. A class of tests for linkage using affected pedigree members. Biometrics 50: 118-127.