Optimizing time histograms for non-Poissonian spike trains

Neural Computation

Volumn 23, Issue 12, 2011, Pages 3125-3144

  Omi, Takahiro ^a   Shinomoto, Shigeru ^a  

^a KYOTO UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

ACTION POTENTIAL; ALGORITHM; ANIMAL; BIOLOGICAL MODEL; CENTRAL NERVOUS SYSTEM; HUMAN; LETTER; NERVE CELL; PHYSIOLOGY; POISSON DISTRIBUTION; REACTION TIME; SIGNAL PROCESSING; TIME;

ACTION POTENTIALS; ALGORITHMS; ANIMALS; CENTRAL NERVOUS SYSTEM; HUMANS; MODELS, NEUROLOGICAL; NEURONS; POISSON DISTRIBUTION; REACTION TIME; SIGNAL PROCESSING, COMPUTER-ASSISTED; TIME FACTORS;

EID: 84856373156     PISSN: 08997667     EISSN: 1530888X     Source Type: Journal    
DOI: 10.1162/NECO_a_00213     Document Type: Letter

References (54)

1. Aalen, O. (1978). Nonparametric inference for a family of counting processes. Annals of Statistics, 6, 701-726.
2. Abeles, M. (1982). Quantification, smoothing, and confidence limits for single-units' histograms. Journal of Neuroscience Methods, 5, 317-325.
3. Adrian, E. D. (1928). The basis of sensation: The action of the sense organs. New York: Norton.
4. Baker, S. N., & Lemon, R. N. (2000). Precise spatiotemporal repeating patterns in monkey primary and supplementary motor areas occur at chance levels. Journal of Neurophysiology, 84, 1770-1780.
5. Barbieri, R., Quirk, M. C., Frank, L. M., Wilson, M. A., & Brown, E. N. (2001). Construction and analysis of non-Poisson stimulus-response models of neural spiking activity. Journal of Neuroscience Methods, 105, 25-37.
6. Berman, M. (1983). Comment on "Likelihood analysis of point processes and its applications to seismological data" by Ogata. Bulletin Internatl. Stat. Instit., 50, 412-418.
7. Bowman, A. W. (1985). A comparative study of some kernel-based nonparametric density estimators. Journal of Statistical Computation and Simulation, 21, 313-327.
8. Britten, K.H., Shadlen, M. N., Newsome, W. T., & Movshon, J. A. (1992). The analysis of visual motion: A comparison of neuronal and psychophysical performance. Journal of Neuroscience, 12, 4745-4765.
9. Britten, K.H., Shadlen, M. N., Newsome, W. T., & Movshon, J. A. (2004). Responses of single neurons inmacaque MT/V5 as a function of motion coherence in stochastic dot stimuli. Neural Signal Archive, NSA2004.1
10. Brown, E. N., Barbieri, R., Ventura, V., Kass, R. E., & Frank, L. M. (2002). The timerescaling theorem and its application to neural spike train data analysis. Neural Computation, 14, 325-346.
11. Cox, D. R. (1962). Renewal theory. London: Chapman and Hall.
12. Cox, D. R., & Lewis, P.A.W. (1966). Statistical analysis of series of events. London: Chapman and Hall.
13. Cunningham, J. P., Gilja, V., Ryu, S. I., & Shenoy, K. V. (2009). Methods for estimating neural firing rates, and their application to brain-machine interfaces. Neural Networks, 22, 1235-1246.
14. Cunningham, J. P., Yu, B. M., Shenoy, K. V., & Sahani, M. (2008). Inferring neural firing rates from spike trains using gaussian processes. In J. Platt, D. Koller, Y. Singer, & S. Roweis (Eds.), Advances in neural information processing systems, 20. Cambridge, MA: MIT Press.
15. Daley, D. J., & Vere-Jones, D. (1988). An introduction to the theory of point processes. New York: Springer-Verlag.
16. Davies, R.M., Gerstein, G. L., & Baker, S. N. (2006).Measurement of time-dependent changes in the irregularity of neural spiking. Journal of Neurophysiology, 96, 906-918.
17. Endres, D., & Oram, M. (2010). Feature extraction from spike trains with Bayesian binning: "Latency is where the signal starts." Journal ofComputational Neuroscience, 29, 149-169.
18. Endres, D., Oram, M., Schindelin, J., & Foldiak, P. (2008). Bayesian binning beats approximate alternatives: Estimating peristimulus time histograms. In J. C. Platt, D. Koller, Y. Singer, & S. Roweis (Eds.), Advances in neural information processing systems, 20. Cambridge, MA: MIT Press.
19. Fano, U. (1947). Ionization yield of radiations, II. The fluctuations of the number of ions. Physical Review, 72, 26-29.
20. Gerstein, G. L., & Kiang, N.Y.S. (1960). An approach to the quantitative analysis of electrophysiological data from single neurons. Biophysical Journal, 1, 15-28.
21. Grün, S. (2009). Data-driven significance estimation for precise spike correlation. Journal of Neurophysiology, 101, 1126-1140.
22. Hall, P. (1990). Akaike's information criterion and Kullback-Leibler loss for histogram density estimation. Probability Theory and Related Fields, 85, 449-467.
23. Holt, G. R., Softky, W. R., Koch, C., & Douglas, R. J. (1996). Comparison of discharge variability in vitro and in vivo in cat visual cortex neurons. Journal of Neurophysiology, 75, 1806-1814.
24. Jacobs, A. L., Fridman, G., Douglas, R. M., Alam, N. M., Latham, P. E., Prusky, G. T., et al. (2009). Ruling out and ruling in neural codes. Proceedings of the National Academy of Sciences of the United States of America, 106, 5936-5941.
25. Kass, R. E., Ventura, V., & Brown, E. N. (2005). Statistical issues in the analysis of neuronal data. Journal of Neurophysiology, 94, 8-25.
26. Kanazawa, Y. (1993). Hellinger distance and Akaike's information criterion for the histogram. Statistics and Probability Letters, 17, 293-298.
27. Kostal, L., & Lánský, P. (2006). Classification of stationary neuronal activity according to its information rate. Network: Computation in Neural Systems, 17, 193-210.
28. Koyama, S., & Shinomoto, S. (2004). Histogram bin width selection for timedependent Poisson processes. Journal of Physics A-Mathematical and General, 37, 7255-7265.
29. Koyama, S., & Shinomoto, S. (2005). Empirical Bayes interpretations of random point events. Journal of Physics A-Mathematical and General, 38, L531-L537.
30. Kuffler, S. W., Fitzhugh, R., & Barlow, H. B. (1957). Maintained activity in the cat's retina in light and darkness. Journal of General Physiology, 40, 683-702.
31. Louis, S., Gerstein, G. L., Grün, S., & Diesmann, M. (2010). Surrogate spike train generation through dithering in operational time. Frontiers in Computational Neuroscience, 4, 127.
32. Miura, K., Okada, M., & Amari, S. (2006). Estimating spiking irregularities under changing environments. Neural Computation, 18, 2359-2386.
33. Nawrot, M. P. (2010). Analysis and interpretation of interval and count variability in neural spike trains. In S. Grün & S. Rotter (Eds.), Analysis of parallel spike trains. New York: Springer.
34. Nawrot, M. P., Boucsein, C., Rodriguez Molina, V., Riehle, A., Aertsen, A., & Rotter, S. (2008). Measurement of variability dynamics in cortical spike trains. Journal of Neuroscience Methods, 169, 374-390.
35. Ogata, Y. (1988). Statistical models for earthquake occurrences and residual analysis for point processes. Journal of American Statistical Association, 83, 9-27.
36. Oram, M.W., Wiener, M. C., Lestienne, R., & Richmond, B. J. (1999). Stochastic nature of precisely timed spike patterns in visual system neuronal responses. Journal of Neurophysiology, 81, 3021-3033.
37. Pillow, J. W., Paninski, L., Uzzell, V. J., Simoncelli, E. P., & Chichilnisky, E. J. (2005). Prediction and decoding of retinal ganglion cell responses with a probabilistic spiking model. Journal of Neuroscience, 25, 11003-11013.
38. Reich, D. S., Victor, J. D., & Knight, B. W. (1998). The power ratio and the interval map: Spiking models and extracellular recordings. Journal of Neuroscience, 18, 10090-10104.
39. Révész, P. (1968). The laws of large numbers. Orlando, FL: Academic Press.
40. Rieke, F., Warland, D., de Ruyter van Steveninck, R., & Bialek, W. (1997). Spikes: Exploring the neural code. Cambridge, MA: MIT Press.
41. Rudemo, M. (1982). Empirical choice of histograms and kernel density estimators. Scandinavian Journal of Statistics, 9, 65-78.
42. Scott, D. W. (1979). Optimal and data-based histograms. Biometrika, 66, 605-610.
43. Shimazaki, H., & Shinomoto, S. (2007). A method for selecting the bin size of a time histogram. Neural Computation, 19, 1503-1527.
44. Shimazaki, H., & Shinomoto, S. (2010). Kernel bandwidth optimization in spike rate estimation. Journal of Computational Neuroscience, 29, 171-182.
45. Shimokawa, T., & Shinomoto, S. (2009). Estimating instantaneous irregularity of neuronal firing. Neural Computation, 21, 1931-1951.
46. Shimokawa, T, Koyama, S., & Shinomoto, S. (2010). A characterization of the timerescaled gamma process as a model for spike trains. Journal of Computational Neuroscience, 29, 183-191.
47. Shinomoto, S. (2010). Estimating the firing rate. In S. Grün & S. Rotter (Eds.), Analysis of parallel spike trains. New York: Springer.
48. Shinomoto, S., Kim, H., Shimokawa, T., Matsuno, N., Funahashi, S., Shima, K., et al. (2009). Relating neuronal firing patterns to functional differentiation of cerebral cortex. PLoS Computational Biology, 5, e1000433.
49. Shinomoto, S., & Koyama, S. (2007). A solution to the controversy between rate and temporal coding. Statistics in Medicine, 26, 4032-4038.
50. Shinomoto, S., Miyazaki, Y., & Tamura, H., & Fujita, I. (2005). Regional and laminar differences in vivo firing patterns of primate cortical neurons. Journal of Neurophysiology, 94, 567-575.
51. Shinomoto, S., Shima, K., & Tanji, J. (2003). Differences in spiking patterns among cortical neurons. Neural Computation, 15, 2823-2842.
52. Smith, A. C., & Brown, E. N. (2003). Estimating a state-space model from point process observations. Neural Computation, 15, 965-991.
53. Snyder, D. L. (1975). Random point processes. Hoboken, NJ: Wiley.
54. Zhao, X., Omi, T., Matsuno, N., & Shinomoto, S. (2010). A non-universal aspect in the temporal occurrence of earthquakes. New Journal of Physics, 12, 063010.