The Annals of Statistics

Some theoretical results on neural spike train probability models

Hock Peng Chan and Wei-Liem Loh

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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.

Article information

Source
Ann. Statist. Volume 35, Number 6 (2007), 2691-2722.

Dates
First available in Project Euclid: 22 January 2008

Permanent link to this document
http://projecteuclid.org/euclid.aos/1201012977

Digital Object Identifier
doi:10.1214/009053607000000280

Mathematical Reviews number (MathSciNet)
MR2382663

Zentralblatt MATH identifier
1129.62101

Subjects
Primary: 62E20: Asymptotic distribution theory
Secondary: 62G20: Asymptotic properties 62M20: Prediction [See also 60G25]; filtering [See also 60G35, 93E10, 93E11]

Keywords
Boundary crossing probability conditional intensity counting process importance sampling neural spike train Poisson process scan statistics sieve maximum likelihood estimation template matching

Citation

Chan, Hock Peng; Loh, Wei-Liem. Some theoretical results on neural spike train probability models. Ann. Statist. 35 (2007), no. 6, 2691--2722. doi:10.1214/009053607000000280. http://projecteuclid.org/euclid.aos/1201012977.


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