Generalized Fisher information matrix in nonextensive systems with spatial correlation.
By using the q -Gaussian distribution derived by the maximum entropy method for spatially correlated N -unit nonextensive systems, we have calculated the generalized Fisher information matrix of gthetanthetam for (theta1,theta2,theta3)=(muq,sigmaq2,s) , where muq, sigmaq2, and s denote the mean, variance, and degree of spatial correlation, respectively, for a given entropic index q . It has been shown from the Cramér-Rao theorem that (1) an accuracy of an unbiased estimate of muq is improved (degraded) by a negative (positive) correlation s, (2) that of sigmaq2 is worsen with increasing s, and (3) that of s is much improved for s approximately= -1/(N-1) or s approximately 1.0 though it is worst at s=(N-2)/2(N-1). Our calculation provides a clear insight to the long-standing controversy whether the spatial correlation is beneficial or detrimental to decoding in neuronal ensembles. We discuss also a calculation of the q-Gaussian distribution applying the superstatistics to the Langevin model subjected to spatially correlated inputs.
Hasegawa
Hideo
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Department of Physics, Tokyo Gakugei University, Koganei, Tokyo 184-8501, Japan. hideohasegawa@goo.jp
D001921:Brain / Q000502:physiology*; D003198:Computer Simulation; D008959:Models, Neurological; D015233:Models, Statistical; D009415:Nerve Net / Q000502:physiology*; D013223:Statistics as Topic