Keiji Miura, Masato Okada, Shun-ichi Amari
We considered a gamma distribution of interspike intervals as a statisti- cal model for neuronal spike generation. The model parameters consist of a time-dependent ﬁring rate and a shape parameter that characterizes spiking irregularities of individual neurons. Because the environment changes with time, observed data are generated from the time-dependent ﬁring rate, which is an unknown function. A statistical model with an unknown function is called a semiparametric model, which is one of the unsolved problem in statistics 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 analytically obtained an optimal estimating function 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.