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Estimating Spiking Irregularities Under Changing Environments

miura{at}ton.scphys.kyoto-u.ac.jp Department of Physics, Kyoto University, Kyoto 606-8502, and Intelligent Cooperation and Control, PRESTO, JST, Chiba 277-8561, Japan

Masato Okada

okada{at}k.u-tokyo.ac.jp Department of Complexity Science and Engineering, University of Tokyo, Chiba 277-8561; Intelligent Cooperation and Control, PRESTO, JST, Chiba 277-8561; and Brain Science Institute, RIKEN, Saitama 351-0198, Japan

Shun-ichi Amari

amari{at}brain.riken.jp Brain Science Institute, RIKEN, Saitama 351-0198, Japan

We considered a gamma distribution of interspike intervals as a statistical model for neuronal spike generation. A gamma distribution is a natural extension of the Poisson process taking the effect of a refractory period into account. The model is specified by two parameters: a time-dependent firing rate and a shape parameter that characterizes spiking irregularities of individual neurons. Because the environment changes over time, observed data are generated from a model with a time-dependent firing rate, which is an unknown function. A statistical model with an unknown function is called a semiparametric model and is generally very difficult to solve. We used a novel method of estimating functions in information geometry to estimate the shape parameter without estimating the unknown function. We obtained an optimal estimating function analytically for the shape parameter independent of the functional form of the firing rate. This estimation is efficient without Fisher information loss and better than maximum likelihood estimation. We suggest a measure of spiking irregularity based on the estimating function, which may be useful for characterizing individual neurons in changing environments.

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