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Title: Some theoretical results on neural spike train probability models
Authors: Chan, H.P. 
Loh, W.-L. 
Keywords: Boundary crossing probability
Conditional intensity
Counting process
Importance sampling
Neural spike train
Poisson process
Scan statistics
Sieve maximum likelihood estimation
Template matching
Issue Date: Dec-2007
Citation: Chan, H.P., Loh, W.-L. (2007-12). Some theoretical results on neural spike train probability models. Annals of Statistics 35 (6) : 2691-2722. ScholarBank@NUS Repository.
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. © Institute of Mathematical Statistics, 2007.
Source Title: Annals of Statistics
ISSN: 00905364
DOI: 10.1214/009053607000000280
Appears in Collections:Staff Publications

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