Semi-parametric dynamic time series modelling with applications to detecting neural dynamics

Annals of Applied Statistics

Volumn 3, Issue 4, 2009, Pages 1776-1804

  Rigat, Fabio ^a   Smith, Jim Q ^a  

^a UNIVERSITY OF WARWICK   (United Kingdom)

Author keywords

Bayesian statistics; Change point testing; Dynamic time series modeling; Statistics for neural data

Indexed keywords

EID: 78650798347     PISSN: 19326157     EISSN: 19417330     Source Type: Journal    
DOI: 10.1214/09-AOAS275     Document Type: Article

References (102)

1. Akaike, H. (1978). On the likelihood of a time series model. The Statistician 27217-235.
2. Akaike, H. (1981). Likelihood of a model and information criteria. J. Econometrics 16 3-14.
3. Albert, J. H. and Chib, S. (1993). Bayes inference via Gibbs sampling for autoregressive time series subject to Markov mean and variance shifts. J. Bus. Econom. Statist. 11 1-15.
4. Barbieri, M. M. and Berger, J. O. (2004). Optimal predictive model selection. Ann. Statist. 32 870-897.
5. Barnard, G. A. (1959). Control charts and stochastic processes. J. Roy. Statist. Soc. Ser. B 21 239-271.
6. Bayarri, M. J. and Berger, J. O. (2004). The interplay between Bayesian and frequentist analysis. Statist. Sci. 19 58-80.
7. Bayarri, M. J. and Morales, J. (2003). Bayesian measures of surprise for outlier detection. J. Statist. Plann. Inference 111 3-22.
8. Bélisle, P., Joseph, L., MacGibbon, B., Wolfson, D. B. and du Berger, R. (1998). Change-point analysis of neuron spike train data. Biometrics 54 113-123.
9. Bengtsson, T. and Cavanaugh, J. E. (2006). An improved Akaike information criterion for state-space model selection. Comput. Statist. Data Anal. 502635-2654.
10. Berger, J. O. and Bayarri, M. L. (1997). Measures of surprise in Bayesian analysis. ISDS Discussion Paper 46, Duke Univ.
11. Berger, J. O., Brown, L. and Wolpert, R. L. (1994). A unified conditional frequentist and Bayesian test for fixed and sequential hypothesis testing. Ann. Statist. 22 1787-1807.
12. Bernardo, J. (1979). Expected information as expected utility. Ann. Statist. 7686-690.
13. Bernardo, J. M. and Smith, A. F. M. (2007). Bayesian Theory. Wiley, Chichester, UK.
14. Box, G. E. P. (1980). Sampling and Bayes' inference in scientific modelling and robustness. J. Amer. Statist. Assoc. 143 383-430.
15. Brillinger, D. R. (1988). Some statistical methods for random processes data from seismology and neurophysiology. Ann. Statist. 16 1-54.
16. Brown, E. N. and Barbieri, R. (2006). Dynamic analyses of neural representations using the state-space modeling paradigm. In: The Cell Biology of Addiction (B. Madras, M. Von Zastrow, C. Colvis, J. Rutter, D. Shurtleff and J. Pollock, eds.). Cold Spring Harbor Laboratory Press, New York.
17. Brown, E., Kass, R. E. and Mitra, P. P. (2004). Multiple neural spike train data analysis: State-of-the-art and future challenges. Nature Neuroscience 7456-461.
18. Buzsáki, G. (2004). Large scale recording of neuronal ensembles. Nature Neuroscience 7 446-451.
19. Cappe, O., Moulines, E. and Ryden, T. (2005). Inference in Hidden Markov Models. Springer, New York.
20. Carlin, B. P., Gelfand, A. E. and Smith, A. F. M. (1992). Hierarchical Bayesian analysis of changepoint problems. App. Statist. 41 389-405.
21. Carota, C., Parmigiani, G. and Polson, N. (1996). Diagnostic measures for model criticism. J. Amer. Statist. Assoc. 91 753-762.
22. Chib, S. (1995). Marginal likelihood from the Gibbs output. J. Amer. Statist. Assoc. 90 1313-1321.
23. Chib, S. (1998). Estimation and comparison of multiple change-point models.J. Econometrics 86 221-241.
24. Critchley, F., Marriott, P. and Salmon, M. (1994). Preferred point geometry and the local differential geometry of the Kullback-Leibler divergence. Ann. Statist. 22 1587-1602.
25. Dawid, A. P. (1984). Present position and potential developments: Some personal views. Statistical theory: The prequential approach. J. Roy. Statist. Soc. Ser. A 147 278-292.
26. Delorme, A., Makeig, S., Fabre-Thorpe, M. and Sejnowski, T. J. (2002). From single trial EEG to brain area dynamics. Neurocomputing 44 1057-1064.
27. Diaconis, P. and Ylvisaker, D. (1979). Conjugate priors for exponential families. Ann. Statist. 7 269-281.
28. Doucet, A., De Freitas, N. and Gordon, N. J. (2001). Sequential Monte Carlo Methods in Practice. Springer-Verlag, New York.
29. Eden, U. T. and Brown, E. N. (2008). Continuous-time filters for state estimation from point process models of neural data. Statist. Sinica.
30. Eden, U. T., Frank, L. M., Barbieri, R., Solo, V. and Brown, E. N. (2004). Dynamic analysis of neural encoding by point process adaptive filtering. Neural Comput. 16 971-998.
31. Fearnhead, P. and Liu, Z. (2007). On-line inference for multiple change points. J. Roy. Statist. Soc. Ser. B 69 589-605.
32. Ferger, D. (1995). Nonparametric tests for nonstandard change-point problems. Ann. Statist. 23 1848-1861.
33. Fienberg, S. E. (1974). Stochastic models for single neuron firing trains: A survey. Biometrics 30 399-427.
34. Frühwirth-Shnatter, S. (1995). Bayesian model discrimination and Bayes factors for linear Gaussian state-space models. J. Roy. Statist. Soc. Ser. B1 237-246.
35. Frühwirth-Shnatter, S. (2001). Markov chain Monte Carlo estimation of classical and dynamic switching and mixture models. J. Amer. Statist. Assoc. 96 194-209.
36. Frühwirth-Shnatter, S. (2006). Finite Mixture and Markov Switching Models. Springer, New York.
37. Gamerman, D. (1992). A dynamic approach to the statistical analysis of point processes. Biometrika 79 39-50.
38. Geisser, S. and Eddy, W. F. (1979). A predictive approach to model selection.J. Amer. Statist. Assoc. 74 153-160.
39. Gelfand, A. E. and Dey, E. K. (1994). Bayesian model choice: Asymptotics and exact calculations. J. Amer. Statist. Assoc. 56 501-514.
40. Gelfand, A. E. and Smith, A. F. M. (1990). Sampling-based approaches to calculating marginal densities. J. Amer. Statist. Assoc. 85 398-409.
41. Gelman, A., Meng, X. L. and Stern, H. S. (1996). Posterior predictive assessment of model fitness via realized discrepancies. Statist. Sinica 6733-807.
42. Ghahramani, Z. and Hinton, G. E. (2000). Variational learning for switching state-space models. Neural Comput. 12 831-864.
43. Goutis, C. and Robert, C. (1998). Model choice in generalised linear models: A Bayesian approach via Kullback-Leibler projections. Biometrika 85 29-37.
44. Gutiérrez-Peña, E. (1997). Moments for the canonical parameter of an exponential family under a conjugate distribution. Biometrika 84 727-732.
45. Guttman, I. (1967). The use of the concept of a future observation in goodness-of-fit problems. J. Roy. Statist. Soc. Ser. B 29 83-100.
46. Hall, P. (1987). On Kullback-Leibler loss and density estimation. Ann. Statist.15 1491-1519.
47. Hamilton, J. D. (1990). Analysis of time series subject to changes in regime. J. Econometrics 45 39-70.
48. Hamilton, J. D. (1994). Time Series Analysis. Princeton Univ. Press, New Jersey.
49. Han, C. and Carlin, B. P. (2001). Markov chain Monte Carlo methods for computing Bayes factors: A comparative review. J. Amer. Statist. Assoc.96 1122-1132.
50. Härdle, W., Lütkepohl, H. and Chen, R. (1997). A review of nonparametric time series analysis. International Statistical Review 65 49-72.
51. Harrison, P. J. and Stevens, C. F. (1976). Bayesian forecasting. J. Roy. Statist. Soc. Ser. B 38 205-247.
52. Hastie, T. (1987). A closer look at the deviance. Amer. Statist. 41 16-20.
53. Iyengar, S. (2001). The analysis of multiple neural spike trains. In Advances in Methodological and Applied Aspects of Probability and Statistics (N. Bolakrishnan, ed.) 507-524. Taylor and Francis, New York.
54. Kalman, R. E. (1960). A new approach to linear filtering and prediction problems. Journal of Basic Engineering 82 35-45.
55. Kass, R. E., Ventura, V. and Brown, E. (2005). Statistical issues in the analysis of neuronal data. Journal of Neurophysiology 94 8-25.
56. Kemp, K. W. (1957). Formulae for calculating the operating characteristic and the average sample number of some sequential tests. J. Roy. Statist. Soc. Ser. B 20 379-386.
57. Kendrick, K. M., da Costa, A. P., Leigh, A. E., Hinton, M. R. and Peirce, J. W. (2001). Sheep don't forget a face. Nature 414 165-166.
58. Kim, C. J. (1994). Dynamic linear models with Markov-switching. J. Econometrics 60 1-22.
59. Koyama, S., Perez-Bolde, L. C. and Kass, R. E. (2008). Approximate methods for state-space models: The Laplace-Gaussian filter. Submitted for publication.
60. Kuhnert, P. M., Mergesen, K. and Tesar, P. (2003). Bridging the gap between different statistical approaches: An integrated framework for modelling. International Statistical Review 71 335-368.
61. Kullback, S. (1997). Information Theory and Statistics. Dover, New York.
62. Kullback, S. and Leibler, R. A. (1951). On information and sufficiency. Ann. Math. Statist. 22 79-86.
63. Lindley, D. (1956). On a measure of the information provided by an experiment. Ann. Math. Statist. 27 986-1005.
64. Loader, C. R. (1996). Change point estimation using nonparametric regression. Ann. Statist. 24 1667-1678.
65. Makeig, S., Westerfield, M., Jung, T. P., Enghoff, S., Towsend, J., Courchesne, E. and Sejnowski, T. J. (2002). Dynamic brain sources of visual evoked responses. Science 295 690-694.
66. Marjoram, P., Molitor, J., Plagnol, V. and Tavaré, S. (2003). Markov chain Monte Carlo without likelihoods. Proc. Natl. Acad. Sci. USA 100 15324-15328.
67. McCulloch, R. E. (1988). Information and the likelihood function in exponential families. Amer. Statist. 42 73-75.
68. McCulloch, R. E. and Tsay, R. S. (1994). Statistical analysis of economic time series via Markov switching models. J. Time Ser. Anal. 15 523-539.
69. Meng, X. L. (1994). Posterior predictive p-values. Ann. Statist. 22 1142-1160.
70. Mira, A. and Petrone, S. (1996). Bayesian hierarchical nonparametric inference for change point problems. Bayesian Statistics 5 693-703.
71. Muller, H. G. (1992). Change-points in nonparametric regression analysis. Ann. Statist. 20 737-761.
72. Newton, M. A. and Raftery, A. E. (1994). Approximate Bayesian inference by the weighted likelihood bootstrap. J. Roy. Statist. Soc. Ser. B 56 3-56.
73. O'Hagan, T. and Forster, J. (1999). Kendall's Advanced Theory of Statistics 2B. Arnold, London, UK.
74. Okatan, M., Wilson, M. A. and Brown, E. N. (2005). Analysing functional connectivity using a network likelihood model of ensemble neural spiking activity. Neural Comput. 17 1927-1961.
75. Page, E. S. (1954). An improvement to Wald's approximation for some properties of sequential tests. J. Roy. Statist. Soc. Ser. B 16 136-139.
76. Page, E. S. (1955). A test for a change in a parameter occurring at an unknown point. Biometrika 42 523-527.
77. Page, E. S. (1961). Cumulative sum charts. Technometrics 3 1-9.
78. Plesser, H. E. and Gerstner, W. (2000). Niose in integrate-and-fire neurons: From stochastic input to escape rates. Neural Comput. 12 367-384.
79. Rao, R. P. N. (2005). Hierarchical Bayesian inference in networks of spiking neurons. In Advances in NIPS 17. MIT Press, MA.
80. Rigat, F., de Gunst, M. and ven Pelt, J. (2006). Bayesian modelling and analysis of spatio-temporal neuronal networks. Bayesian Anal. 1 733-764.
81. Robert, C. P., Celeux, G. and Diebolt, J. (1993). Bayesian estimation of hidden Markov chains: A stochastic implementation. Statist. Probab. Lett. 16 77-83.
82. Robinson, P. M. (1983). Non-parametric estimation for time series models. J. Time Ser. Anal. 4 185-208.
83. Rubin, D. B. (1984). Bayesianly justifiable and relevant frequency calculations for the applied statistician. Ann. Statist. 12 1151-1172.
84. San Martini, A. and Spezzaferri, F. (1984). A predictive model selection criterion. J. Roy. Statist. Soc. Ser. B 46 296-383.
85. Shumway, R. H. and Stoffer, D. S. (1991). Dynamic linear models with switching. J. Amer. Statist. Assoc. 86 763-769.
86. Smith, A. C., Loren, M. F., Wyrth, S., Yanike, M., Hu, D., Kubota, Y., Graybiel, A. M., Suzuki, W. A. and Brown, E. M. (2004). Dynamic analysis of learning in behavioural experiments. Journal of Neuroscience 24 447-461.
87. Smith, A. F. M. (1975). A Bayesian approach to inference about a change-point in a sequence of random variables. Biometrika 62 407-416.
88. Smith, A. F. M. and Roberts, G. O. (1993). Bayesian computations via the Gibbs sampler and related Markov chain Monte Carlo methods. J. Roy. Statist. Soc. Ser. B 55 3-23.
89. Smith, J. Q. (1990). Non-linear state space models with partially specified distributions on states. J. Forecast. 9 137-149.
90. Smith, J. Q. (1992). A comparison of the characteristics of some Bayesian forecasting models. International Statistical Reviews 60 75-85.
91. Spiegelhalter, D. J., Best, N. G., Carlin, P. B. and van der Linde, A. (2002). Bayesian measures of model complexity and fit. J. Roy. Statist. Soc. Ser. B64 583-639.
92. Srinivansan, L., Eden, U. T., Willsky, A. S. and Brown, E. N. (2006). A state-space analysis for reconstruction of goal-directed movements using neural signals. Neural Comput. 18 2465-2494.
93. Stephens, D. A. (1994). Bayesian retrospective multiple-changepoint identification. App. Statist. 43 159-178.
94. Stone, M. (1959). Application of a measure of information to the design and comparison of regression experiments. Ann. Math. Statist. 30 55-70.
95. Tierney, L. (1994). Markov chains for exploring posterior distributions. Ann. Statist. 22 1701-1762.
96. Tierney, L. and Kadane, J. B. (1986). Accurate approximations for posterior moments and marginal densities. J. Amer. Statist. Assoc. 81 84-86.
97. Truccolo, W., Eden, U. T., Fellows, M. R., Donoghue, J. P. and Brown, E. N. (2005). A point process framework for relating neural spiking activity to spiking history, neural ensemble and extrinsic covariate effects. Journal of Neurophysiology 93 1074-1089.
98. West, M. (1986). Bayesian model monitoring. J. Roy. Statist. Soc. Ser. B 4870-78.
99. West, M. and Harrison, P. J. (1986). Monitoring and adaptation in Bayesian forecasting models. J. Amer. Statist. Assoc. 81 741-750.
100. West, M. and Harrison, P. J. (1997). Bayesian Forecasting and Dynamic Models, 2nd ed. Springer, New York.
101. West, M., Harrison, P. J. and Migon, H. S. (1985). Dynamic generalised linear models and Bayesian forecasting. J. Amer. Statist. Assoc. 80 73-83.
102. Wirth, S., Yanike, M., Loren, M. F., Smith, A. C., Brown, E. M. and Suzuki, W. A. (2003). Single neurons in the monkey hippocampus and learning of new associations. Science 300 1578-1584.