## Electronic Journal of Statistics

### Introduction to neural spike train data for phase-amplitude analysis

#### Abstract

Statistical analysis of spike trains is one of the central problems in neural coding, and can be pursued in several ways. One option is model-based, i.e. assume a parametric or semi-parametric model, such as the Poisson model, for spike train data and use it in decoding spike trains. The other option is metric-based, i.e. choose a metric for comparing the numbers and the placements of spikes in different trains, and does not need a model. A prominent idea in the latter approach is to derive metrics that are based on measurements of time-warpings of spike trains needed in the alignments of corresponding spikes. We propose the use of ideas developed in functional data analysis, namely the definition and separation of phase-amplitude components, as a novel tool for analyzing spike trains and decoding underlying neural signals. For concreteness, we introduce a real spike train dataset taken from experimental recordings of the primary motor cortex of a monkey while performing certain arm movements. To facilitate functional data analysis, one needs to smooth the observed discrete spike trains with Gaussian kernels.

#### Article information

Source
Electron. J. Statist., Volume 8, Number 2 (2014), 1759-1768.

Dates
First available in Project Euclid: 29 October 2014

https://projecteuclid.org/euclid.ejs/1414588160

Digital Object Identifier
doi:10.1214/14-EJS865

Mathematical Reviews number (MathSciNet)
MR3273592

Zentralblatt MATH identifier
1305.62332

#### Citation

Wu, Wei; Hatsopoulos, Nicholas G.; Srivastava, Anuj. Introduction to neural spike train data for phase-amplitude analysis. Electron. J. Statist. 8 (2014), no. 2, 1759--1768. doi:10.1214/14-EJS865. https://projecteuclid.org/euclid.ejs/1414588160

#### References

• [1] Aronov, D. and Victor, J., Non-Euclidean properties of spike train metric spaces., Physical Review E, 69, 061905, 2004.
• [2] Box, G. E. P., Hunter, W. G., and Hunter, J. S., Statistics for Experimenters: An Introduction to Design, Data Analysis, and Model Building. New York: Wiley, 1978.
• [3] Brown, E. N., Barbieri, R., Ventura, V., Kass, R. E., and Frank, L. M., The time-rescaling theorem and its applicationto neural spike train data analysis., Neural Computation, 14:325–346, 2002.
• [4] Dayan, P. and Abbott, L. F., Theoretical Neuroscience: Computational and Mathematical Modeling of Neural Systems. The MIT Press, 2001.
• [5] Dubbs, A. J., Seiler, B. A., and Magnasco, M. O., A fast $L^p$ spike alighment metric., Neural Computation, 22 :2785–2808, 2010.
• [6] Houghton, C. and Sen, K., A new multineuron spike train metric., Neural Computation, 20 :1495–1511, 2008.
• [7] Kass, R. E. and Ventura, V., A spike-train probability model., Neural Computation, 13 :1713–1720, 2001.
• [8] Kass, R. E., Ventura, V., and Brown, E. N., Statistical issues in the analysis of neuronal data., Journal of Neurophysiology, 94:8–25, 2005.
• [9] Lim, D. and Capranica, R. R., Measurement of temporal regularity of spike train responses in auditory nerve fibers of the green treefrog., Journal of Neurosceince Methods, 52:203–213, 1994.
• [10] Ramsay, J. O. and Silverman, B. W., Functional Data Analysis, Second Edition. Springer Series in Statistics, 2005.
• [11] Rieke, F., Warland, D., Ruyter van Steveninck, R. R., and Bialek, W., Spikes: Exploring the Neural Code. MIT Press, 1997.
• [12] van Rossum, M. C. W., A novel spike distance., Neural Computation, 13:751–763, 2001.
• [13] Victor, J. D., Goldberg, D. H., and Gardner, D., Dynamic programming algorithms for comparing multineuronal spike trains via cost-based metrics and alignments., Journal of Neuroscience Methods, 161:351–360, 2007.
• [14] Victor, J. D. and Purpura, K. P., Nature and precision of temporal coding in visual cortex: A metric-space analysis., Journal of Neurophysiology, 76 :1310–1326, 1996.
• [15] Wu, W. and Srivastava, A., An information-geometric framework for statistical inferences in the neural spike train space., Journal of Computational Neuroscience, 31:725–748, 2011.
• [16] Wu, W. and Srivastava, A., Estimating summary statistics in the spike-train space., Journal of Computational Neuroscience, 34:391–410, 2013.