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Stochastic Methods in Neuroscience$
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Carlo Laing and Gabriel J Lord

Print publication date: 2009

Print ISBN-13: 9780199235070

Published to Oxford Scholarship Online: February 2010

DOI: 10.1093/acprof:oso/9780199235070.001.0001

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Statistical Models of Spike Trains

Statistical Models of Spike Trains

(p.272) 10 Statistical Models of Spike Trains
Stochastic Methods in Neuroscience

Liam Paninski

Emery N. Brown

Satish Iyengar

Robert E. Kass

Oxford University Press

Spiking neurons make inviting targets for analytical methods based on stochastic processes: spike trains carry information in their temporal patterning, yet they are often highly irregular across time and across experimental replications. The bulk of this volume is devoted to mathematical and biophysical models useful in understanding neurophysiological processes. In this chapter we consider statistical models for analysing spike train data. We focus on the stochastic integrate-and-fire neuron as a particularly useful model, which may be approached analytically in three distinct ways: via the language of (1) stochastic (diffusion) processes, (2) hidden Markov (state-space) models, and (3) point processes. Each of these viewpoints comes equipped with its own specialized tools and insights, and the power of the IF model is most evident when all of these tools may be brought to bear simultaneously.

Keywords:   Fokker–Planck equation, integrate-and-fire, state-space model, renewal process, diffusion model, inverse Gaussian, first passage time, spike-triggered average

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