Blocking Gibbs sampling for linkage analysis in large pedigrees with many loops

American Journal of Human Genetics

Volumn 65, Issue 3, 1999, Pages 885-901

  Jensen, Claus Skaanning ^a   Kong, Augustine ^b  

^a AALBORG UNIVERSITY   (Denmark)

^b UNIVERSITY OF CHICAGO   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; BAYES THEOREM; COMPUTER PROGRAM; DIAGNOSTIC PROCEDURE; GENETIC ANALYSIS; GENETIC LINKAGE; HUMAN; HUMAN CELL; INTERMETHOD COMPARISON; MAJOR CLINICAL STUDY; MATHEMATICAL COMPUTING; PEDIGREE; PRIORITY JOURNAL;

EID: 0033358743     PISSN: 00029297     EISSN: None     Source Type: Journal    
DOI: 10.1086/302524     Document Type: Article

References (42)

1. Andersen SK, Olesen KG, Jensen FV, Jensen F (1989) HUGIN - a shell for building Bayesian belief universes for expert systems. In: Sridharan NS (ed) Proceedings of the Eleventh International Joint Conference on Artificial Intelligence. Morgan Kaufmann, San Mateo, CA, pp 1080-1085
2. Bennett CH (1976) Efficient estimation of free energy differences from Monte Carlo data. J Comput Physics 22:245-268
3. Cannings C, Thompson EA, Skolnick MH (1976) The recursive derivation of likelihoods on complex pedigrees. Adv Appl Prob 8:622-625
4. _ (1978) Probability functions on complex pedigrees. Adv Appl Prob 10:26-61
5. Cottingham RW Jr, Idury RM, Schäffer AA (1993) Faster sequential genetic linkage computations. Am J Hum Genet 53:252-263
6. Dawid AP (1992) Applications of a general propagation algorithm for probabilistic expert systems. Stat Comput 2:25-36
7. Elston RC, Stewart J (1971) A general model for the genetic analysis of pedigree data. Hum Hered 21:523-542
8. Gelfand AE, Smith AFM (1990) Sampling-based approaches to calculating marginal densities. J Am Stat Assoc 85(410):398-409
9. Gelman A, Meng XL (1994) Path sampling for computing normalizing constants: identities and theory. Tech rep 376. Department of Statistics, University of Chicago, Chicago
10. _ (1998) Simulating normalizing constants: from importance sampling to bridge sampling to path sampling. Stat Sci 13(2): 163-185
11. Gelman A, Rubin DB (1992) Inference from iterative simulation using single and multiple sequences. Stat Sci 7: 457-511
12. Geman S, Geman D (1984) Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images. IEEE Trans Pattern Anal Machine Intell 6:721-741
13. Geyer CJ (1991) Markov chain Monte Carlo Maximum likelihood. In: Keramidas E (ed) Computing science and statistics: proceedings of the 23d Symposium on the Interface. Inteface Foundation of North America, Fairfax Station, VA, pp 156-163
14. _ (1992) Practical Markov Chain Monte Carlo. Stat Sci 7(4): 473-511
15. Geyer CJ, Thompson EA (1993) Annealing Markov chain Monte Carlo with applications to pedigree analysis. Res rep 589, School of Statistics, University of Minnesota, Minneapolis
16. Irwin M, Cox N, Kong A (1994) Sequential imputation for multilocus linkage analysis. Proc Natl Acad Sci USA 91: 11684-11688.
17. Jensen CS (1996a) A simple method for finding a legal configuration in complex Bayesian networks. Tech rep R-96-2046, Department of Computer Science, Aalborg University, Aalborg, Denmark
18. _ (1997) Blocking Gibbs sampling for interference in large and complex Bayesian networks with applications in genetics. PhD thesis, Department of Computer Science, Aalborg University, Aalborg, Denmark
19. Jensen CS, Kong A, Kjærulff U (1995) Blocking-Gibbs sampling in very large probabilistic expert systems. Int J Hum Comput Stud 42:647-666
20. Jensen CS, Sheehan N (1998) Problems with determination of noncommunicating classes for Monte Carlo Markov chain applications in pedigree analysis. Biometrics 54:416-425
21. Jensen FV (1996b) An introduction to Bayesian networks. UCL Press/Springer-Verlag, New York
22. Jensen FV, Lauritzen SL, Olesen KG (1990) Bayesian updating in causal probabilistic networks by local computations. Comput Stat Q 4:269-282
23. Kjærulff U (1993) Approximation of Bayesian networks through edge removals. Res rep IR-93-2007, Department of Computer Science, Aalborg University, Aalborg, Denmark
24. Kong A (1991) Efficient methods for computing linkage likelihoods of recessive diseases in inbred pedigrees. Genet Epidemiol 8:81-103
25. Kong A, Cox N, Frigge M, Irwin M (1993) Sequential imputation and multipoint linkage analysis. Genet Epidemiol 10:483-488
26. Lange K, Elston RC (1975) Extensions to pedigree analysis. I. Likelihood calculations for simple and complex pedigrees. Hum Hered 25:95-105
27. Lathrop GM, Lalouel JM (1984) Easy calculations of lod scores and genetic risks on small computers. Am J Hum Genet 36:460-465
28. Lathrop GM, Lalouel JM, Julier C, Ott J (1985) Multilocus linkage analysis in humans: detection of linkage and estimation of recombination. Am J Hum Genet 37:482-498
29. Lauritzen SL (1992) Propagation of probabilities, means and variances in mixed graphical association models. J Am Stat Assoc 87:1098-1108
30. Lauritzen SL, Spiegelhalter DJ (1988) Local computations with probabilities on graphical structures and their application to expert systems. J R Stat Soc [B] 50(2): 157-224
31. Lin S, Thompson E, Wijsman E (1994) Finding noncommunicating sets for Markov chain Monte Carlo estimations on pedigrees. Am J Hum Genet 54:695-704
32. Meng XL, Schilling S (1996) Fitting full-information item factor models and an empirical investigation of bridge sampling. J Am Stat Assoc 91:1254-1267
33. Meng XL, Wong WH (1996) Simulating ratios of normalizing constants via simple identity: A theoretical exploration. Stat Sin 6:831-860
34. Pearl J (1986) Fusion, propagation and structuring in belief networks. Artificial Intell 29:241-288
35. _ (1991) Probabilistic reasoning in intelligent systems: networks of plausible inference series in representation and reasoning, 2d ed. Morgan Kaufmann, San Mateo, CA
36. Schäffer AA, Gupta SK, Shriram K, Cottingham RW Jr (1994) Avoiding recomputation in linkage analysis. Hum Hered 44: 225-237
37. Shachter RD, Andersen SK, Szolovits P (1994) Global conditioning for probabilistic inference in belief networks. In: Lopez de Mantaras R, Poole D (eds) Proceedings of the Tenth Conference on Uncertainty in Artificial Intelligence. Morgan Kaufmann, San Mateo, CA, pp 514-522
38. Sheehan N, 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
39. Shenoy PP, Shafer GR (1990) Axioms for probability and belief-function propagation. In: Shachter RD, Levitt TS, Kanal LN, Lemmer JF (eds) Uncertainty in artificial intelligence. Vol 4. Elsevier Science (North-Holland), Amsterdam, pp 169-198
40. Smith AFM, Roberts GO (1993) Bayesian computation via the Gibbs sampler and related Markov chain Monte Carlo methods. J R Stat Soc [B] 55(1): 5-23
41. Thomas A, Spiegelhalter DJ, Gilks WR (1992) BUGS: A program to perform Bayesian inference using Gibbs sampling. In: Bernardo JM, Berger JO, Dawid AP, Smith AFM (eds) Bayesian statistics. Vol 4. Clarendon Press, Oxford, pp 837-842
42. Thomas DC, Cortessis V (1992) A Gibbs sampling approach to linkage analysis. Hum Hered 42:63-76