Bayesian restoration of a Hidden Markov chain with applications to DNA sequencing

Journal of Computational Biology

Volumn 6, Issue 2, 1999, Pages 261-277

  Churchill, Gary A ^a   Lazareva, Betty ^b  

^a JACKSON LABORATORY   (United States)

^b Molecular Applications Group   (United States)

Author keywords

Bayesian inference; Hidden Markov model; Monte Carlo Markov chain; Sequence alignment

Indexed keywords

ARTICLE; BAYES THEOREM; DNA SEQUENCE; MOLECULAR INTERACTION; PRIORITY JOURNAL; PROBABILITY; SEQUENCE ANALYSIS; SYSTEM ANALYSIS;

EID: 0033060905     PISSN: 10665277     EISSN: None     Source Type: Journal    
DOI: 10.1089/cmb.1999.6.261     Document Type: Article

References (39)

1. Allison, L., and Wallace, C.S. 1994. Posterior distribution of alignments and its application to parameter estimation of evolutionary trees and to optimization of multiple alignments. J. Mol. Evol. 39, 418-430.
2. Baldi, P., Chauvin, Y., Hunkapillar, T., and McClure, M.A. 1994. Hidden Markov models of biological primary sequence information. Proc. Nat. Acad. Sci. U.S.A. 91, 1059-1063.
3. Baum, L.E., and Petrie, T. 1966. Statistical inference for probabilistic of finite state Markov chains. Ann. Math. Stat. 37, 1554-1563.
4. Baum, L.E., Petrie, T., Soules, G., and Weiss, N. 1970. A maximization technique occurring in the statistical analysis of probabilistic functions of Markov chains. Ann. Math. Stat. 41, 164-171.
5. Casella, G., and Robert, C.P. 1996. Rao-Blackwellization of sampling schemes. Biometrika 83, 81-94.
6. Churchill, G.A. 1989. A stochastic model for heterogeneous DNA sequences. Bull. Math. Biol. 51, 79-94.
7. Churchill, G.A. 1992. Hidden Markov chains and the analysis of genome structure. Comput. Chem. 16, 107-115.
8. Churchill, G.A. 1995. Accurate restoration of DNA sequences, 90-148. In Gatsaris, C., Hodges, J.S., Kass, R.E., and Singpur-walla, N.D. eds., Case Studies in Bayesian Statistics. Vol. II. Springer-Verlag, New York.
9. Dempster, A.P., Laird, N.M., and Rubin, D.B. 1977. Maximum likelihood from incomplete data via EM algotithm. J. R. Stat. Soc. B 39, 1-38.
10. Eddy, S.R. 1995. Multiple alignment using hidden Markov models, 114-120. In: Rawlings, C., et al., eds., Proc. of the Third International Conference on Intelligent Systems for Molecular Biology. AAAI Press, Menlo Park, CA.
11. Eddy, S.R. 1996. Hidden Markov models. Curr. Opin. Struct. Biol. 6, 361-365.
12. Elliot, R.J., Aggoun, L., and Moore, J.B. 1994. Hidden Markov Models: Estimation and Control. Vol. 29. Applications of Mathematics. Springer-Verlag, New York.
13. Fredkin, D.R., and Rice, J.A. 1992a. Maximum likelihood estimation and identification directly from single-channel recordings. Proc. R. Soc. Lond. B 249, 125-132.
14. Fredkin, D.R., and Rice, J. 1992b. Bayesian restoration of single channel patch clamp recordings. Biometrics 48, 427-448.
15. Gelfand, A.E., and Smith, A.F.M. 1990. Sampling based approaches to calculating marginal densities. J. Am. Stat. Assoc. 85, 398-409.
16. Gelman, A., and Rubin, D.B. 1992. Inference from iterative simulation using multiple sequences. Stat. Sci. 7, 457-511.
17. Geman, S., and Geman, D. 1984. Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images. I.E.E.E. Trans. Pattern Analysis Machine Intellig. 6, 721-741.
18. Geyer, C.J., and Thompson, E.A. 1995. Annealing Markov chain Monte Carlo with applications to ancestral inference. J. Am. Stat. Assoc. 90, 909-920.
19. Huang, X. 1992. A contig assembly program based on sensitive detection of fragment overlaps. Genomics 14, 18-25.
20. Hunkapillar, T., Kaiser, R.J., Koop, B.F., and Hood, L. 1991. Large-scale automated DNA sequence determination. Science 254, 59-67.
21. Juang, B.H., and Rabiner, L.R. 1990. The segmental k-means algorithm for estimating parameters of hidden Markov models. I.E.E.E. Trans. Acoustics Speech Signal Processing 38, 1639-1641.
22. Juang, B.H., and Rabiner, L.R. 1991. Hidden Markov models for speech recognition. Technometrics 33, 251-272.
23. Krogh, A., Brown, M., Mian, I.S., Sjölander, K., and Haussler, D. 1994. Hidden Markov models in computational biology: applications to protein modeling. J. Mol. Biol. 235, 1501-1531.
24. Lawrence, C.E., Altschul, S.F., Boguski, M.S., Lui, J.S., Neuwald, A.F., and Wootton, J.C. 1993. Detecting subtle sequence signals: a Gibss sampling strategy for multiple alignment. Science 262, 208-214.
25. Leroux, B.G. 1992. Maximum-likelihood estimation for hidden Markov models. Stochastic Processes Appl. 40, 127-143.
26. Liu, J.S., and Lawrence, C.E. 1995a. Statistical models for multiple sequence alignment: Unifications and generalizations. Proc. Stat. Comput. A.S.A. Section 21, 1-8.
27. Liu, J.S., Neuwald, A.F., and Lawrence, C.E. 1995b. Bayesian models for local multiple sequence alignment and Gibbs sampling strategies. J. Am. Stat. Assoc. 90, 1156-1170.
28. Merkav, N., and Ephraim, Y. 1991. Maximum likelihood hidden Markov modeling using a dominant sequence of states. I.E.E.E. Trans. Signal Processing 39, 2111-2115.
29. Rabiner, L.R. 1989. A tutorial on hidden Markov models and selected applications in speech recognition. Proc. I.E.E.E. 77, 257-286.
30. Ripley, B.D. 1987. Stochastic Simulation. Wiley, New-York.
31. Robert, C.P., Celeux, G., and Diebolt, J. 1994. Bayesian estimation of hidden Markov chains: a stochastic implementation. Stat. Probabil. Lett. 16, 77-83.
32. Robert, C.P. 1994. The Bayesian Choice. Springer-Verlag, New York.
33. Seto, D., Koop, B.F., and Hood, L. 1993. An experimentally derived data set constructed for testing large-scale DNA sequence assembly algorithms. Genomics 15, 673-676.
34. Sjölander, K., Karplus, K., Brown, M., et al. 1996. Dirichlet mixtures: a method for improved detection of weak but significant protein sequence homology. C.A.B.I.O.S. 12, 327-345.
35. Stratanovich, R.L. 1960. Conditional Markov processes. Theory Probabil. Appl. 5, 156-178.
36. Tanner, M., and Wong, W. 1987. "The calculation of posterior distribution by data augmentation. J. Am. Stat. Assoc. 82, 528-550.
37. Viterbi, J. 1967. Error bounds for convolutional codes and an asymptotically optimal decoding algorithm. I.E.E.E. Trans. Information Theory 13, 260-269.
38. Waterman, M.S. 1995. Introduction to Computational Biology. Chapman and Hall, London.
39. White, J.V., Stultz, C.M., and Smith, T.F. 1994. Protein classification by stochastic modeling and optimal filtering of amino acid sequences. Math. Biosci. 119, 35-75.