TY - GEN

T1 - Unbiased estimator of shape parameter for spiking irregularities under changing environments

AU - Miura, Keiji

AU - Okada, Masato

AU - Amari, Shun Ichi

PY - 2005/12/1

Y1 - 2005/12/1

N2 - We considered a gamma distribution of interspike intervals as a statistical 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.

AB - We considered a gamma distribution of interspike intervals as a statistical 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.

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M3 - Conference contribution

AN - SCOPUS:37249039836

SN - 9780262232531

T3 - Advances in Neural Information Processing Systems

SP - 891

EP - 898

BT - Advances in Neural Information Processing Systems 18 - Proceedings of the 2005 Conference

T2 - 2005 Annual Conference on Neural Information Processing Systems, NIPS 2005

Y2 - 5 December 2005 through 8 December 2005

ER -