Some theoretical results on neural spike train probability models

Chan, Hock Peng ; Loh, Wei-Liem

Ann. Statist., Tome 35 (2007) no. 1, p. 2691-2722 / Harvested from Project Euclid

Résumé

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.

Détail

Publié le : 2007-12-15
Classification:  Boundary crossing probability,  conditional intensity,  counting process,  importance sampling,  neural spike train,  Poisson process,  scan statistics,  sieve maximum likelihood estimation,  template matching,  62E20,  62G20,  62M20