Statistical Models of Spike Trains

Stochastic Methods in Neuroscience

Volumn , Issue , 2010, Pages

  Paninski, Liam ^a   Brown, Emery N ^b,c   Iyengar, Satish ^d   Kass, Robert E ^e  

^a Department of Statistics Center for Theoretical Neuroscience Columbia University ^*  (United States)

^b MASSACHUSETTS GENERAL HOSPITAL   (United States)

^c MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^d UNIVERSITY OF PITTSBURGH   (United States)

^e CARNEGIE MELLON UNIVERSITY   (United States)

Author keywords

Diffusion model; First passage time; Fokker Planck equation; Integrate and fire; Inverse gaussian; Renewal process; Spike triggered average; State space model

Indexed keywords

EID: 84920751793     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1093/acprof:oso/9780199235070.003.0010     Document Type: Chapter

References (90)

1. Ahmadian, Y., Pillow, J., and Paninski, L. (2008). Efficient Markov chain Monte Carlo methods for decoding population spike trains. Under review, Neural Computation.
2. Badel, L., Richardson, M. J. E., and Gerstner, W. (2006). Dependence of the spiketriggered average voltage on membrane response properties. Neurocomputing, 69, 1062-1065.
3. Barbieri, R., Quirk, M., Frank, L., Wilson, M., and Brown, E. (2001). Construction and analysis of non-poisson stimulus-response models of neural spiking activity. Journal of Neuroscience Methods, 105, 25-37.
4. Brillinger, D. (1988). Maximum likelihood analysis of spike trains of interacting nerve cells. Biological Cybernetics, 59, 189-200.
5. Brillinger, D. (1992). Nerve cell spike train data analysis: a progression of technique. Journal of the American Statistical Association, 87, 260-271.
6. Brown, E. (2005). The theory of point processes for neural systems. In Methods and Models in Neurophysics (ed. C. Chow, B. Gutkin, D. Hansel, C. Meunier, and J. Dalibard), Elsevier, Amsterdam, pp. 691-726.
7. Brown, E., Barbieri, R., Eden, U., and Frank, L. (2003). Likelihood methods for neural data analysis. In Computational Neuroscience: A Comprehensive Approach (ed. J. Feng), CRC Press, Boca Raton, pp. 253-286.
8. Brown, E., Barbieri, R., Ventura, V., Kass, R., and Frank, L. (2002). The time-rescaling theorem and its application to neural spike train data analysis. Neural Computation, 14, 325-346.
9. Brown, E., Frank, L., Tang, D., Quirk, M., and Wilson, M. (1998). A statistical paradigm for neural spike train decoding applied to position prediction from ensemble firing patterns of rat hippocampal place cells. Journal of Neuroscience, 18, 7411-7425.
10. Brown, E., Kass, R., and Mitra, P. (2004). Multiple neural spike train data analysis: stateof- the-art and future challenges. Nature Neuroscience, 7, 456-461.
11. Brown, E., Nguyen, D., Frank, L., Wilson, M., and Solo, V. (2001). An analysis of neural receptive field plasticity by point process adaptive filtering. PNAS, 98, 12261-12266.
12. Brunel, N. and Hakim, V. (1999). Fast global oscillations in networks of integrate-and-fire neurons with low firing rates. Neural Computation, 11, 1621-1671.
13. Brunel, N. and Latham, P. E. (2003). Firing rate of the noisy quadratic integrate-and-fire neuron. Neural Computation, 15, 2281-2306.
14. Buoncore, A., Nobile, A., and Ricciardi, L. (1987). A new integral equation for the evaluation of first-passage-time probability densities. Adv. Appl. Prob., 19, 784-800.
15. Burkitt, A. and Clark, G. (1999). Analysis of integrate-and-fire neurons: synchronization of synaptic input and spike output. Neural Computation, 11, 871-901.
16. Burkitt, A. N. (2006a). A review of the integrate-and-fire neuron model: I. Homogeneous synaptic input. Biological Cybernetics, 95, 1-19.
17. Burkitt, A. N. (2006b). A review of the integrate-and-fire neuron model: II. Inhomogeneous synaptic input and network properties. Biological Cybernetics, 95, 27-12.
18. Burnham, K. and Anderson, D. (2002). Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach. Springer, New York.
19. Carandini, M., Horton, J., and Sincich, L. (2007). Thalamic filtering of retinal spike trains by postsynaptic summation. Journal of Vision, 7, 1-11.
20. Chichilnisky, E. J. (2001). A simple white noise analysis of neuronal light responses. Network: Computation in Neural Systems, 12, 199-213.
21. Chornoboy, E., Schramm, L., and Karr, A. (1988). Maximum likelihood identification of neural point process systems. Biological Cybernetics, 59, 265-275.
22. Czanner, G., Eden, U., Wirth, S., Yanike, M., Suzuki, W., and Brown, E. (2008). Analysis of between-trial and within-trial neural spiking dynamics. Journal of Neurophysiology, 99, 2672-2693.
23. Czanner, G. and Iyengar, S. (2004). Expectation-Maximization (EM) estimation of an integrate-and-fire model with spike-frequency adaptation. COSYNE, presented at the Computational and Systems Neuroscience meeting, Cold Spring Harbor, NY, 2004.%
24. Daniels, H. (1982). Sequential tests contructed from images. Annals of Statistics, 10, 394-400.
25. de la Rocha, J., Doiron, B., Shea-Brown, E., Josic, K., and Reyes, A. (2007). Correlation between neural spike trains increases with firing rate. Nature, 448, 802-806.
26. de Ruyter van Steveninck, R. and Bialek, W. (1988). Real-time performance of a movement-senstivive neuron in the blowfly visual system: coding and information transmission in short spike sequences. Proc. R. Soc. Lond. B, 234, 379-414.
27. Dempster, A., Laird, N., and Rubin, D. (1977). Maximum likelihood from incomplete data via the EM algorithm. Journal Royal Stat. Soc., Series B, 39, 1-38.
28. DiNardo, E., Nobile, A., Pirozzi, E., and Ricciardi, L. (2001). A computational approach to first-passage-time problems for Gauss-Markov processes. Advances in Applied Probability, 33, 453-482.
29. Dombeck, D. A, Khabbaz, A. N, Collman, F., Adelman, T. L., and Tank, D. W. (2007, Oct). Imaging large-scale neural activity with cellular resolution in awake, mobile mice. Neuron, 56(1), 43-57.
30. Ermentrout, G. and Kopell, N. (1986). Parabolic bursting in an excitable system coupled with a slow oscillation. SIAM Journal on Applied Math, 46, 233-253.
31. Fourcaud, N. and Brunel, N. (2002). Dynamics of the firing probability of noisy integrateand- fire neurons. Neural Computation, 14, 2057-2110.
32. Frank, L., Eden, U., Solo, V., Wilson, M., and Brown, E. (2002). Contrasting patterns of receptive field plasticity in the hippocampus and the entorhinal cortex: An adaptive filtering approach. J. Neurosci., 22(9), 3817-3830.
33. Gerstein, G. and Mandelbrot, B. (1964). Random walk models for spike activity of a single neuron. Biophysical Journal, 4, 41-68.
34. Gerstner, W. and Kistler, W. (2002). Spiking Neuron Models: Single Neurons, Populations, Plasticity. Cambridge University Press, Cambridge.
35. Haskell, E., Nykamp, D. Q., and Tranchina, D. (2001). Population density methods for large-scale modelling of neuronal networks with realistic synaptic kinetics: cutting the dimension down to size. Network: Comput. Neural. Syst., 12, 141-174.
36. Huys, Q., Ahrens, M., and Paninski, L. (2006). Efficient estimation of detailed singleneuron models. Journal of Neurophysiology, 96, 872-890.
37. Huys, Q.J.M. and Paninski L. (2009). Smoothing of, and Parameter Estimation from, Noisy Biophysical Recordings. PLoS Comput Biol 5 (5): e1000379.
38. Iyengar, S. (1985). Hitting lines with two-dimensional Brownian motion. SIAM Journal on Applied Mathematics, 45, 983-989.
39. Iyengar, S. and Liao, Q. (1997). Modeling neural activity using the generalized inverse Gaussian distribution. Biological Cybernetics, 77, 289-295.
40. Izhikevich, E. (2007). Dynamical Systems in Neuroscience. MIT Press, Cambridge MA.
41. Jolivet, R., Lewis, T., and Gerstner, W. (2004). Generalized integrate-and-fire models of neuronal activity approximate spike trains of a detailed model to a high degree of accuracy. Journal of Neurophysiology, 92, 959-976.
42. Karatzas, I. and Shreve, S. (1997). Brownian Motion and Stochastic Calculus. Springer, Berlin.
43. Kass, R. and Ventura, V. (2001). A spike-train probability model. Neural Comp., 13, 1713-1720.
44. Kass, R. E., Ventura, V., and Brown, E. N. (2005). Statistical issues in the analysis of neuronal data. J. Neurophysio., 94, 8-25.
45. Keat, J., Reinagel, P., Reid, R., and Meister, M. (2001). Predicting every spike: a model for the responses of visual neurons. Neuron, 30, 803-817.
46. Knight, B. W. (1972). Dynamics of encoding in a population of neurons. Journal of General Physiology, 59, 734-766.
47. Knight, B. W., Omurtag, A., and Sirovich, L. (2000). The approach of a neuron population firing rate to a new equilibrium: an exact theoretical result. Neural Computation, 12, 1045-1055.
48. Koyama, S. and Kass, R. (2008). Spike train probability models for stimulus-driven leaky integrate-and-fire neurons. Neural Computation, 20(7), 1776-1795.
49. Koyama, S., Kass, R., and Paninski, L. (2008). Efficient computation of the most likely path in integrate-and-fire and more general state-space models. COSYNE.
50. Kulkarni, J. and Paninski, L. (2007). Common-input models for multiple neural spike-train data. Network: Computation in Neural Systems, 18, 375-407.
51. Lansky, P., Sanda, P., and He, J. (2006). The parameters of the stochastic leaky integrateand- fire neuronal model. Journal of Computational Neuroscience, 21, 211-223.
52. Mainen, Z. and Sejnowski, T. (1995). Reliability of spike timing in neocortical neurons. Science, 268, 1503-1506.
53. Moreno, R., de la Rocha, J., Renart, A., and Parga, N. (2002). Response of spiking neurons to correlated inputs. Physical Review Letters, 89, 288101.
54. Mullowney, P. and Iyengar, S. (2007). Parameter estimation for a leaky integrate-and-fire neuronal model from ISI data. Journal of Computational Neuroscience, 24, 179-194.
55. Nikitchenko, M. and Paninski, L. (2007). An expectation-maximization Fokker-Planck algorithm for the noisy integrate-and-fire model. COSYNE, presented at the Computational and Systems Neuroscience meeting, Salt Lake City, UT 2007.
56. Nykamp, D. Q. and Tranchina, D. (2000). A population density approach that facilitates large-scale modeling of neural networks: Analysis and an application to orientation tuning. Journal of Computational Neuroscience, 8, 19-50.
57. Okatan, M., Wilson, M., and Brown, E. (2005). Analyzing functional connectivity using a network likelihood model of ensemble neural spiking activity. Neural Computation, 17, 1927-1961.
58. Paninski, L. (2004). Maximum likelihood estimation of cascade point-process neural encoding models. Network: Computation in Neural Systems, 15, 243-262.
59. Paninski, L. (2005). Log-concavity results on Gaussian process methods for supervised and unsupervised learning. Advances in Neural Information Processing Systems, 17.
60. Paninski, L. (2006a). The most likely voltage path and large deviations approximations for integrate-and-fire neurons. Journal of Computational Neuroscience, 21, 71-87.
61. Paninski, L. (2006b). The spike-triggered average of the integrate-and-fire cell driven by Gaussian white noise. Neural Computation, 18, 2592-2616.
62. Paninski, L., Fellows, M., Shoham, S., Hatsopoulos, N., and Donoghue, J. (2004). Superlinear population encoding of dynamic hand trajectory in primary motor cortex. J. Neurosci., 24, 8551-8561.
63. Paninski, L., Haith, A., and Szirtes, G. (2008). Integral equation methods for computing likelihoods and their derivatives in the stochastic integrate-and-fire model. Journal of Computational Neuroscience, 24, 69-79.
64. Paninski, L., Pillow, J., and Lewi, J. (2007). Statistical models for neural encoding, decoding, and optimal stimulus design. In Computational Neuroscience: Progress in Brain Research (ed. P. Cisek, T. Drew, and J. Kalaska). Elsevier, Amsterdam.
65. Paninski, L., Pillow, J., and Simoncelli, E. (2004a). Comparing integrate-and-fire models estimated using intracellular and extracellular data. Neurocomputing, 65, 379-385.
66. Paninski, L., Pillow, J., and Simoncelli, E. (2004b). Maximum likelihood estimation of a stochastic integrate-and-fire neural model. Neural Computation, 16, 2533-2561.
67. Pillow, J. and Paninski, L. (2007). Model-based decoding, information estimation, and change-point detection in multi-neuron spike trains. Under review, Neural Computation.
68. Pillow, J., Paninski, L., Uzzell, V., Simoncelli, E., and Chichilnisky, E. J. (2005). Prediction and decoding of retinal ganglion cell responses with a probabilistic spiking model. Journal of Neuroscience, 25, 11003-11013.
69. Pillow, J., Shlens, J., Paninski, L., Simoncelli, E., and Chichilnisky, E. J. (2008). Visual information coding in multi-neuronal spike trains. Nature, 454, 995-999.
70. Plesser, H. and Tanaka, S. (1997). Stochastic resonance in a model neuron with reset. Physics Letters A, 225, 228-234.
71. Press, W., Teukolsky, S., Vetterling, W., and Flannery, B. (1992). Numerical recipes in C. Cambridge University Press, Cambridge.
72. Rabiner, L. (1989). A tutorial on hidden Markov models and selected applications in speech recognition. Proceedings of the IEEE, 77, 257-286.
73. Reich, D., Victor, J., and Knight, B. (1998). The power ratio and the interval map: Spiking models and extracellular recordings. The Journal of Neuroscience, 18, 10090-10104.
74. Ricciardi, L. (1977). Diffusion Processes and Related Topics in Biology. Springer, Berlin.
75. Rieke, F., Warland, D., de Ruyter van Steveninck, R., and Bialek, W. (1997). Spikes:Exploring the Neural Code. MIT Press, Cambridge, MA.
76. Risken, H. (1996). The Fokker-Planck equation: Methods of Solutions and Applications. Springer-Verlag, New York.
77. Schnitzer, M. and Meister, M. (2003). Multineuronal firing patterns in the signal from eye to brain. Neuron, 37, 499-511.
78. Seshadri, V. (1998). The Inverse Gaussian Distribution. Springer, Berlin.
79. Siegert, A. (1951). On the first passage time probability problem. Physical Review, 81, 617-623.
80. Simoncelli, E., Paninski, L., Pillow, J., and Schwartz, O. (2004). Characterization of neural responses with stochastic stimuli. In The Cognitive Neurosciences (3rd edn) (ed. M. Gazzaniga). MIT Press, Cambridge, MA.
81. Smith, A. and Brown, E. (2003). Estimating a state-space model from point process observations. Neural Computation, 15, 965-991.
82. Snyder, D. and Miller, M. (1991). Random Point Processes in Time and Space. Springer-Verlag, New York.
83. Srinivasan, L., Eden, U., Willsky, A., and Brown, E. (2006). A state-space analysis for reconstruction of goal-directed movements using neural signals. Neural Computation, 18, 2465-2494.
84. Stein, R. (1965). A theoretical analysis of neuronal variability. Biophysical Journal, 5, 173-194.
85. Stevens, C. and Zador, A. (1998). Novel integrate-and-fire-like model of repetitive firing in cortical neurons. Proc. 5th joint symp. neural computation, UCSD.
86. Truccolo, W., Eden, U., Fellows, M., Donoghue, J., and Brown, E. (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.
87. Tuckwell, H. (1989). Stochastic Processes in the Neurosciences. SIAM, Philadelphia.
88. Ventura, V., Cai, C., and Kass, R. (2005). Trial-to-trial variability and its effect on timevarying dependence between two neurons. Journal of Neurophysiology, 94, 2928-2939.
89. Vogelstein, J. and Paninski, L. (2009). Model-based optimal inference of spike times and calcium dynamics given noisy and intermittent calcium-fluorescence imaging. Biophysical Journal, in press.
90. Yu, B., Afshar, A., Santhanam, G., Ryu, S., Shenoy, K., and Sahani, M. (2006). Extracting dynamical structure embedded in neural activity. Advances in Neural Information Processing Systems, 18, 1545-1552.