Statistical analysis of hierarchical structure of neural spike trains

2014 Fiscal Year Final Research Report

• Project/Area Number: 24700287
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Statistical science
• Research Institution: The Institute of Statistical Mathematics
• Principal Investigator: KOYAMA Shinsuke 統計数理研究所, 大学共同利用機関等の部局等, 准教授 (20589999)
• Project Period (FY): 2012-04-01 – 2015-03-31
• Keywords: スパイク時系列解析 / 点過程 / ゆらぎのスケーリング則 / 積分発火モデル

Outline of Final Research Achievements

We propose a statistical framework for modeling the non-Poisson variability of spike trains observed in a wide range of brain regions. Central to our approach is the assumption that the variance and the mean of ISIs are related by a power function characterized by two parameters: the scale factor and exponent. This single assumption allows the variability of spike trains to have an arbitrary scale and various dependencies on the firing rate in the spike count statistics, as well as in the interval statistics, depending on the two parameters of the power function. On the basis of this statistical assumption, we show that the power function relationship between the mean and variance of ISIs with various exponents emerges in a leaky integrate-and-fire model under certain conditions. We also propose a statistical model for spike trains that exhibits the variance-to-mean power relationship, and a maximum likelihood method is developed for inferring the parameters.

Free Research Field

統計神経科学