Seven things to remember about hidden Markov models: A tutorial on Markovian models for time series

Journal of Mathematical Psychology

Volumn 55, Issue 6, 2011, Pages 403-415

  Visser, Ingmar ^a  

^a UNIVERSITY OF AMSTERDAM   (Netherlands)

Author keywords

Dependent mixture model; Hidden Markov model; Mixture model

Indexed keywords

EID: 82755182723     PISSN: 00222496     EISSN: 10960880     Source Type: Journal    
DOI: 10.1016/j.jmp.2011.08.002     Document Type: Review

References (78)

1. Agresti A. Categorical data analysis. Wiley series in probability and mathematical statistics 2002, Wiley-Interscience, Hoboken, NJ. 2 ed.
2. Al-Ani T. Using hidden Markov models for sleep disordered breathing identification. Simulation Modelling Practice and Theory 2004, 12:117-128.
3. Altman R.M. Mixed hidden Markov models. Journal of the American Statistical Association 2007, 102:201-210.
4. Bartolucci, F., Farcomeni, A., & Pennoni, F. 2010. An overview of latent Markov models for longitudinal categorical data. Arxiv preprint arxiv:1003.2804.
5. Bartolucci F., Lupparelli M., Montanari G. Latent Markov model for longitudinal binary data: an application to the performance evaluation of nursing homes. The Annals of Applied Statistics 2009, 3:611-636.
6. Bartolucci F., Pennoni F., Francis B. A latent Markov model for detecting patterns of criminal activity. Journal of the Royal Statistical Society: Series A Statistics in Society 2007, 170:115-132.
7. Bartolucci F., Solis-Trapala I.L. Multidimensional latent Markov models in a developmental study of inhibitory control and attentional flexibility in early childhood. Psychometrika 2010, 75:725-743.
8. Batchelder W. An all-or-none theory for learning on both the paired-associate and concept levels. Journal of Mathematical Psychology 1970, 7:97-117.
9. Baum L.E., Petrie T. Statistical inference for probabilistic functions of finite state Markov chains. Annals of Mathematical Statistics 1966, 67:1554-1563.
10. Bijleveld C.C., Mooijaart A. Latent Markov modelling of recidivism data. Statistica Neerlandica 2003, 57:305-320.
11. Böckenholt U. Measuring change: mixed Markov models for ordinal panel data. British Journal of Mathematical and Statistical Psychology 1999, 52:125-136.
12. Böckenholt U. A latent Markov model for the analysis of longitudinal data collected in continuous time: states, durations, and transitions. Psychological Methods 2005, 10:65-83.
13. Bollen K.A. Latent variables in psychology and the social sciences. Annual Review of Psychology 2002, 53:605-634.
14. Bower G.H., Trabasso T. Concept identification. Studies in mathematical psychology 1964, 32-94. Stanford University Press. R.C. Atkinson (Ed.).
15. Bulla J., Berzel A. Computational issues in parameter estimation for stationary hidden Markov models. Computational Statistics 2008, 23:1-18.
16. Bulla J., Bulla I. Stylized facts of financial time series and hidden semi-Markov models. Computational Statistics & Data Analysis 2006, 51:2192-2209.
17. Bulla, J., Mergner, S., Bulla, I., Sesboue, A., & Chesneau, C. 2011. Markov-switching asset allocation: do profitable strategies exist? Journal of Asset Management(in press).
18. Cappe O., Moulines E., Ryden T. Inference in hidden Markov models. Springer series in statistics 2005, Springer, New York.
19. Chung H., Walls T., Park Y. A latent transition model with logistic regression. Psychometrika 2007, 72:413-435.
20. Dempster A.P., Laird N.M., Rubin D.B. Maximum likelihood from incomplete data via the em algorithm. Journal of the Royal Statistical Society 1978, 39:1-38. Series B Methodological.
21. Dutilh G., Wagenmakers E.-J., Visser I., van der Maas H.L.J. A phase transition model for the speed-accuracy trade-off in response time experiments. Cognitive Science 2011, 35:211-250.
22. Ephraim Y., Merhav N. Hidden Markov processes. IEEE Transactions on Information Theory 2002, 48:1518-1569.
23. Flexer A., Sykacek P., Rezek I., Dorffner G. An automatic, continuous and probabilistic sleep stager based on a hidden Markov model. Applied Artificial Intelligence 2002, 16:199-207.
24. Forney Jr G.D. The viterbi algorithm. Proceedings of the IEEE 1973, 61:268-278.
25. Frühwirth-Schnatter S. Finite mixture and Markov switching models. Springer series in statistics 2006, Springer.
26. Ghahramani Z. An introduction to hidden Markov models and Bayesian networks. IJPRAI 2001, 15:9-42.
27. Ghysels E. On the periodic structure of the business cycle. Journal of Business and Economic Statistics 1994, 12:289-298.
28. Giudici P., Ryden T., Vandekerkhove P. Likelihood-ratio tests for hidden Markov models. Biometrics 2000, 56:742-747.
29. Guedon Y. Exploring the state sequence space for hidden Markov and semi-Markov chains. Computational Statistics & Data Analysis 2007, 51:2379-2409.
30. Hamaker E. Using information criteria to determine the number of regimes in threshold autoregressive models. Journal of Mathematical Psychology 2009, 53:518-529.
31. Hamilton J. A new approach to the economic analysis of nonstationary time series and the business cycle. Econometrica: Journal of the Econometric Society 1989, 57:357-384.
32. Harte, D. 2010. HiddenMarkov: Hidden Markov Models. R package version 1. 3-1.
33. Hughes J., Guttorp P. A class of stochastic models for relating synoptic atmospheric patterns to regional hydrologic phenomena. Water Resources Research 1994, 30:1535-1546.
34. Hughes J., Guttorp P., Charles S. A non-homogeneous hidden Markov model for precipitation occurrence. Journal of the Royal Statistical Society: Series C Applied Statistics 1999, 48:15-30.
35. Jackson, C. 2010. msm: Multi-state Markov and hidden Markov models in continuous time. R package version 0.9.7.
36. Jelinek F. Continuous speech recognition by statistical methods. Proceedings of the IEEE 1976, 64:532-556.
37. Juang B., Rabiner L. The segmental K-means algorithm for estimating parameters of hidden Markov models. Acoustics, Speech and Signal Processing, IEEE Transactions on 1990, 38:1639-1641.
38. Kaplan D. An overview of Markov chain methods for the study of stage-sequential developmental processes. Developmental Psychology 2008, 44:457-467.
39. Kemeny J.G., Snell J. Finite Markov chains 1960, Princeton, Van Nostrand.
40. Kim C.-J. Dynamic linear models with Markov-switching. Journal of Econometrics 1994, 60:1-22.
41. Kintsch W., Morris C.J. Application of a Markov model to free recall and recognition. Journal of Experimental Psychology 1965, 69:200-206.
42. Krogh A. An introduction to hidden Markov models for biological sequences. Computational methods in molecular biology 1998, 45-63. Elsevier, Amsterdam, (chapter 4). S.L. Salzberg, D.B. Searls, S. Kasif (Eds.).
43. Langeheine R. Manifest and latent Markov chain models for categorical panel data. Journal of Educational and Behavioral Statistics 1988, 13:299.
44. Langeheine R., Van de Pol F. A unifying framework for Markov modeling in discrete space and discrete time. Sociological Methods and Research 1990, 18:416-441.
45. Langeheine R., Van de Pol F. Fitting higher order Markov chains. Methods of Psychological Research Online 2000, 5:32-55.
46. Leroux B.G., Puterman M.L. Maximum-penalized-likelihood estimation for independent and Markov-dependent mixture models. Biometrics 1992, 48:545-548.
47. Liechty J., Pieters R., Wedel M. Global and local covert visual attention: evidence from a Bayesian hidden Markov model. Psychometrika 2003, 68:519-541.
48. Lystig T.C., Hughes J.P. Exact computation of the observed information matrix for hidden Markov models. Journal of Computational and Graphical Statistics 2002.
49. Mackay R.J. Estimating the order of a hidden Markov model. Canadian Journal of Statistics 2002, 30:573-589.
50. Mackay Altman R. Assessing the goodness-of-fit of hidden Markov models. Biometrics 2004, 60:444-450.
51. McLachlan G.J., Krishnan T. The EM algorithm and extensions 1997, John Wiley & sons, New York.
52. McLachlan G.J., Peel D. Finite mixture models. Wiley series in probability and mathematical statistics 2000, Wiley-Interscience, New York etc.
53. Miller G.A. Finite Markov processes in psychology. Psychometrika 1952, 17:149-167.
54. Molenaar P. A manifesto on psychology as ideographic science: bringing the person back into scientific psychology, this time forever. Measurement 2004, 2:201-218.
55. Otterpohl J. A constrained HMM-based approach to the estimation of perceptual switching dynamics in pigeons. Neurocomputing 2001, 38-40:1495-1501.
56. Pew R. The speed-accuracy operating characteristic. Acta Psychologica 1969, 30:16-26.
57. Qin F. Restoration of single-channel currents using the segmental k-means method based on hidden Markov modeling. Biophysical Journal 2004, 86:1488-1501.
58. Rabiner L.R. A tutorial on hidden Markov models and selected applications in speech recognition. Proceedings of IEEE 1989, 77:267-295.
59. R Development Core Team 2010. R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0.
60. Schmittmann V.D., Dolan C.V., van der Maas H.L.J., Neale M.C. Discrete latent Markov models for normally distributed response data. Multivariate Behavioral Research 2005, 40:461-488.
61. Schmittmann V.D., Visser I., Raijmakers M.E.J. Multiple learning modes in the development of rule-based category-learning task performance. Neuropsychologia 2006, 44:2079-2091.
62. Schwarz G. Estimating the dimension of a model. Annals of Statistics 1978, 6:461-464.
63. Taramasco, O. 2009. RHmm: hidden Markov models simulations and estimations. R package version 1.3.1.
64. Titman A.C., Sharples L.D. A general goodness-of-fit test for Markov and hidden Markov models. Statistics in Medicine 2008, 27:2177-2195.
65. Turner R. Direct maximization of the likelihood of a hidden Markov model. Computational Statistics & Data Analysis 2008, 52:4147-4160.
66. Vermunt J.K., Langeheine R., Böckenholt U. Discrete-time discrete-state latent Markov modles with time-constant and time-varying covariates. Journal of Educational and Behavioral Statistics 1999, 24:179-207.
67. Visser I. Book review of Zucchini & MacDonald: hidden Markov models for time series: an introduction using R. Journal of Mathematical Psychology 2010, 54:509-511.
68. Visser I., Raijmakers M.E.J., Molenaar P.C.M. Confidence intervals for hidden Markov model parameters. British Journal of Mathematical and Statistical Psychology 2000, 53:317-327.
69. Visser I., Raijmakers M.E.J., Molenaar P.C.M. Fitting hidden Markov models to psychological data. Scientific Programming 2002, 10:185-199.
70. Visser I., Raijmakers M.E.J., Molenaar P.C.M. Characterizing sequence knowledge using online measures and hidden Markov models. Memory & Cognition 2007, 35:1502-1517.
71. Visser I., Speekenbrink M. depmixs4: An R-package for hidden Markov models. Journal of Statistical Software 2010, 36:1-21. R package, current version available from CRAN.
72. Viterbi A. Error bounds for convolutional codes and an asymptotically optimum decoding algorithm. IEEE Transactions on Information Theory 1967, 13:260-269.
73. Wickelgren W. Speed-accuracy tradeoff and information processing dynamics. Acta Psychologica 1977, 41:67-85.
74. Wickens T.D. Models for behavior: stochastic processes in psychology 1982, W. H. Freeman and Company, San Francisco.
75. Wiggins L.M. Panel analysis 1973, Elsevier Scientific Publishing Company.
76. Zucchini W. An introduction to model selection. Journal of Mathematical Psychology 2000, 44:41-61.
77. Zucchini W., MacDonald I. Hidden Markov models for time series: An introduction using R. Number 110 in monographs on statistics and applied probability 2009, CRC Press, Boca Raton.
78. Zucchini W., Raubenheimer D., MacDonald I.L. Modeling time series of animal behavior by means of a latent-state model with feedback. Biometrics 2008, 64:807-815.