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Optimal Signal Estimation in Neuronal Models

Petr Lánsk

lansky{at}biomed.cas.cz, Institute of Physiology, Academy of Sciences of Czech Republic, 142 20 Prague 4, Czech Republic

Priscilla E. Greenwood

pgreenw{at}math.la.asu.edu, Department of Mathematics, Arizona State University, Tempe, AZ, U.S.A.

We study optimal estimation of a signal in parametric neuronal models on the basis of interspike interval data. Fisher information is the inverse asymptotic variance of the best estimator. Its dependence on the parameter value indicates accuracy of estimation. Our models assume that the input signal is estimated from neuronal output interspike interval data where the frequency transfer function is sigmoidal. If the coefficient of variation of the interspike interval is constant with respect to the signal, the Fisher information is unimodal, and its maximum for the most estimable signal can be found. We obtain a general result and compare the signal producing maximal Fisher information with the inflection point of the sigmoidal transfer function in several basic neuronal models.