The effect of interspike interval statistics on the information gain
under the rate coding hypothesis
Pages: 63  80,
Issue 1,
February
2014
doi:10.3934/mbe.2014.11.63 Abstract
References
Full text (509.4K)
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Shinsuke Koyama  The Institute of Statistical Mathematics, 103 Midoricho, Tachikawa, Tokyo 1908562, Japan (email)
Lubomir Kostal  Institute of Physiology, Academy of Sciences of the Czech Republic, Videnska 1083, 14220 Prague, Czech Republic (email)
1 
M. Abramowitz and I. A. Stegun, eds., "Handbook of Mathematical Functions, with Formulas, Graphs, and Mathematical Tables," Dover Publications, Inc., New York, 1966. 

2 
E. D. Adrian, The basis of sensation, Br. Med. J., 1 (1954). 

3 
R. Barbieri, M. C. Quirk, L. M. Frank, M. A. Wilson and E. N. Brown, Construction and analysis of nonPoisson stimulusresponse models of neural spiking activity, Journal of Neuroscience Methods, 105 (2001), 2537. 

4 
M. Berman, Inhomogeneous and modulated gamma processes, Biometrika, 68 (1981), 143152. 

5 
J. M. Bernardo, Reference posterior distributions for Bayesian inference. With discussion, J. Roy. Stat. Soc. B, 41 (1979), 113147. 

6 
A. Bershadskii, E. Dremencov, D. Fukayama and G. Yadid, Probabilistic properties of neuron spiking timeseries obtained in vivo, Eur. Phys. J. B, 24 (2001), 409413. 

7 
G. S. Bhumbra, A. N. Inyushkin and R. E. J. Dyball, Assessment of spike activity in the supraoptic nucleus, J. Neuroendocrinol., 16 (2004), 390397. 

8 
L. BonnasseGahot and J.P. Nadal, Perception of categories: From coding efficiency to reaction times, Brain Res., 1434 (2012), 4761. 

9 
A. Borst and F. E. Theunissen, Information theory and neural coding, Nature Neurosci., 2 (1999), 947958. 

10 
N. Brunel and J.P. Nadal, Mutual information, Fisher information, and population coding, Neural Computation, 10 (1998), 17311757. 

11 
R. S. Chhikara and J. L. Folks, "The Inverse Gaussian Distribution: Theory, Methodology, and Applications," Marcel Dekker, New York, 1989. 

12 
M. Cohen, The fisher information and convexity, IEEE Transactions on Information Theory, 14 (1968), 591592. 

13 
D. R. Cox and P. A. W. Lewis, "The Statistical Analysis of Series of Events," Methuen & Co., Ltd., London; John Wiley & Sons, Inc., New York, 1966. 

14 
J. P. Cunningham, V. Gilja, S. I. Ryu and K. V. Shenoy, Methods for estimating neural firing rates, and their application to brainmachine interfaces, Neural Networks, 22 (2009), 12351246. 

15 
J. P. Cunningham, B. M. Yu, K. V. Shenoy and M. Sahani, Inferring neural firing rates from spike trains using Gaussian processes, in "Neural Information Processing Systems" (eds. J. C. Platt, D. Koller, Y. Singer and S. Roweis), Vol. 20, (2008), 329336. 

16 
D. J. Daley and D. VereJones, "An Introduction to the Theory of Point Processes. Vol. I. Elementary Theory and Methods," Second edition, Probability and its Applications (New York), SpringerVerlag, New York, 2003. 

17 
P. DuchampViret, L. Kostal, M. Chaput, P. Lánsky and J.P. Rospars, Patterns of spontaneous activity in single rat olfactory receptor neurons are different in normally breathing and tracheotomized animals, J. Neurobiology, 65 (2005), 97114. 

18 
R. G. Gallager, "Information Theory and Reliable Communication," John Wiley & Sons, Inc., New York, 1968. 

19 
G. L. Gerstein and B. Mandelbrot, Random walk models for the spike activity of a single neuron, Biophys. J., 4 (1964), 4168. 

20 
I. J. Good, "Probability and the Weighing of Evidence," Charles Griffin & Co., Ltd., London; Hafner Publishing Co., New York, N. Y., 1950. 

21 
I. J. Good and R. A. Gaskins, Nonparametric roughness penalties for probability densities, Biometrika, 58 (1971), 255277. 

22 
P. E. Greenwood and P. Lánský, Optimal signal estimation in neuronal models, Neural Comput., 17 (2005), 22402257. 

23 
P. E. Greenwood and P. Lánský, Optimum signal in a simple neuronal model with signaldependent noise, Biol. Cybern., 92 (2005), 199205. 

24 
P. E. Greenwood, L. M. Ward, D. F. Russell, A. Neiman and F. Moss, Stochastic resonance enhances the electrosensory information available to paddlefish for prey capture, Phys. Rev. Lett., 84 (2000), 47734776. 

25 
A. Grémiaux, T. Nowotny, D. Martinez, P. Lucas and J.P. Rospars, Modelling the signal delivered by a population of firstorder neurons in a moth olfactory system, Brain Res., 1434 (2012), 123135. 

26 
P. J. Huber, "Robust Statistics," Wiley Series in Probability and Mathematical Statistics, John Wiley & Sons, Inc., New York, 1981. 

27 
S. Ikeda and J. H. Manton, Capacity of a single spiking neuron channel, Neural Comput., 21 (2009), 17141748. 

28 
S. Iyengar and Q. Liao, Modeling neural activity using the generalized inverse gaussian distribution, Biological Cybernetics, 77 (1997), 289295. 

29 
B. Jørgensen, "Statistical Properties of the Generalized Inverse Gaussian Distribution," Lecture Notes in Statistics, 9, SpringerVerlag, New YorkBerlin, 1982. 

30 
A. M. Kagan, I. V. Linnik and C. R. Rao, "Characterization Problems in Mathematical Statistics," John Wiley & Sons, New York, 1973. 

31 
R. E. Kass and V. Ventura, A spiketrain probability model, Neural Computation, 13 (2001), 17131720. 

32 
S. M. Kay, "Fundamentals of Statistical Signal Processing: Estimation Theory," Prentice Hall, New Jersey, 1993. 

33 
L. Kostal, Information capacity in the weaksignal approximation, Phys. Rev. E, 82 (2010), 026115. 

34 
L. Kostal, Approximate information capacity of the perfect integrateandfire neuron using the temporal code, Brain Res., 1434 (2012), 136141. 

35 
L. Kostal, P. Lansky and O. Pokora, Variability measures of positive random variables, PLoS ONE, 6 (2011), e21998. 

36 
L. Kostal and O. Pokora, Nonparametric estimation of informationbased measures of statistical dispersion, Entropy, 14 (2012), 12211233. 

37 
S. Koyama, Coding efficiency and detectability of rate fluctuations with nonPoisson neuronal firing, in "Neural Information Processing Systems," Vol. 25, The Institute of Statistical Mathematics, 2013. 

38 
S. Koyama and R. E. Kass, Spike train probability models for stimulusdriven leaky integrateandfire neurons, Neural Computation, 20 (2008), 17761795. 

39 
S. Kullback, "Information Theory and Statistics," Dover Publications, Inc., Mineola, New York, 1968. 

40 
E. L. Lehmann and G. Casella, "Theory of Point Estimation," Second edition, Springer Texts in Statistics, SpringerVerlag, New York, 1998. 

41 
M. W. Levine, The distribution of the intervals between neural impulses in the maintained discharges of retinal ganglion cells, Biol. Cybern., 65 (1991), 459467. 

42 
Z. Pawlas, L. B. Klebanov, M. Prokop and P. Lansky, Parameters of spike trains observed in a short time window, Neural Comput., 20 (2008), 13251343. 

43 
D. H. Perkel and T. H. Bullock, Neural coding, Neurosci. Res. Prog. Sum., 3 (1968), 405527. 

44 
J. W. Pillow, Timerescaling methods for the estimation and assessment of nonPoisson neural encoding models, in "Neural Information Processing Systems" (eds. Y. Bengio, D. Schuurmans, J. Lafferty, C. K. I. Williams and A. Culotta), Vol. 22, (2008), 14731481. 

45 
E. J. G. Pitman, "Some Basic Theory for Statistical Inference," Monographs on Applied Probability and Statistics, Chapman and Hall, London; A Halsted Press Book, John Wiley & Sons, New York, 1979. 

46 
C. Pouzat and A. Chaffiol, Automatic spike train analysis and report generation. An implementation with R, R2HTML and STAR, J. Neurosci. Methods, 181 (2009), 119144. 

47 
D. S. Reich, J. D. Victor and B. W. Knight, The power ratio and the interval map: Spiking models and extracellular recordings, Journal of Neuroscience, 18 (1998), 1009010104. 

48 
B. J. Richmond and L. M. Optican, Temporal encoding of twodimensional patterns by single units in primate inferior temporal cortex. II. Quantification of response waveform, Journal of Neurophysiology, 57 (1987), 147161. 

49 
J. J. Rissanen, Fisher information and stochastic complexity, IEEE Trans. Inf. Theory, 42 (1996), 4047. 

50 
L. J. Savage, "The Foundations of Statistics," John Wiley & Sons, Inc., New York; Chapman & Hill, Ltd., London, 1954. 

51 
H. S. Seung and H. Sompolinsky, Simple models for reading neuronal population codes, Proceedings of the National Academy of Sciences of the United States of America, 90 (1993), 1074910753. 

52 
C. E. Shannon and W. Weaver, "The Mathematical Theory of Communication," University of Illinois Press, Urbana, Illinois, 1949. 

53 
R. B. Stein, The information capacity of nerve cells using a frequency code, Biophys. J., 7 (1967), 797826. 

54 
F. Theunissen and J. P. Miller, Temporal encoding in nervous systems: A rigorous definition, J. Comput. Neurosci., 2 (1995), 149162. 

55 
H. C. Tuckwell, "Introduction to Theoretical Neurobiology, Vol. 2. Nonlinear and Stochastic Theories," Cambridge Studies in Mathematical Biology, 8, Cambridge University Press, Cambridge, 1988. 

56 
A. W. van der Vaart, "Asymptotic Statistics," Cambridge Series in Statistical and Probabilistic Mathematics, 3, Cambridge University Press, Cambridge, 1998. 

57 
K. Zhang and T. Sejnowski, Neural tuning: To sharpen or broaden?, Neural Computation, 11 (1999), 7584. 

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