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December 2007 Some theoretical results on neural spike train probability models
Hock Peng Chan, Wei-Liem Loh
Ann. Statist. 35(6): 2691-2722 (December 2007). DOI: 10.1214/009053607000000280

Abstract

This article contains two main theoretical results on neural spike train models, using the counting or point process on the real line as a model for the spike train. The first part of this article considers template matching of multiple spike trains. P-values for the occurrences of a given template or pattern in a set of spike trains are computed using a general scoring system. By identifying the pattern with an experimental stimulus, multiple spike trains can be deciphered to provide useful information.

The second part of the article assumes that the counting process has a conditional intensity function that is a product of a free firing rate function s, which depends only on the stimulus, and a recovery function r, which depends only on the time since the last spike. If s and r belong to a q-smooth class of functions, it is proved that sieve maximum likelihood estimators for s and r achieve the optimal convergence rate (except for a logarithmic factor) under L1 loss.

Citation

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Hock Peng Chan. Wei-Liem Loh. "Some theoretical results on neural spike train probability models." Ann. Statist. 35 (6) 2691 - 2722, December 2007. https://doi.org/10.1214/009053607000000280

Information

Published: December 2007
First available in Project Euclid: 22 January 2008

zbMATH: 1129.62101
MathSciNet: MR2382663
Digital Object Identifier: 10.1214/009053607000000280

Subjects:
Primary: 62E20
Secondary: 62G20 , 62M20

Keywords: boundary crossing probability , Conditional intensity , counting process , importance sampling , neural spike train , Poisson process , scan statistics , sieve maximum likelihood estimation , template matching

Rights: Copyright © 2007 Institute of Mathematical Statistics

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Vol.35 • No. 6 • December 2007
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