Modulated Renewal Process and Statistical Analysis of Multiple Spike-Trains

Statistical models of spike trains∗

Information and Statistical Structure in Spike Trains

One of the most challenging and fascinating problems in science is deciphering how neural systems encode information. Mathematical models are critical in any effort to determine how neural systems represent and transmit information. Such mathematical approaches span a wide range, which may be divided approximately into two kinds of research activities. The first kind of activity uses detailed b...

Universal Statistical Behavior of Neural Spike Trains

We construct a model that predicts the statistical properties of spike trains generated by a sensory neuron. The model describes the combined e ects of the neuron's intrinsic properties, the noise in the surrounding, and the external driving stimulus. We show that the spike trains exhibit universal statistical behavior over short times, modulated by a strongly stimulus{dependent behavior over l...

Gaussian process modulated renewal processes

Renewal processes are generalizations of the Poisson process on the real line whose intervals are drawn i.i.d. from some distribution. Modulated renewal processes allow these interevent distributions to vary with time, allowing the introduction of nonstationarity. In this work, we take a nonparametric Bayesian approach, modelling this nonstationarity with a Gaussian process. Our approach is bas...

Modeling and Analysis of Neural Spike Trains

1 Department of Statistics, Florida State University, Tallahassee, FL 32306, USA 2Department of Mathematics, The City College of New York, New York, NY 10031, USA 3Department of Psychiatry and Department of Neuroscience and Physiology, New York University School of Medicine, New York, NY 10016, USA 4 School of Design and Human Engineering, Ulsan National Institute of Science and Technology, UNI...