2009/02/28 by Hideo Hasegawa · 2 citations
Computer Science · Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Complex Systems and Time Series Analysis #Correlation #Entropy (arrow of time) #Fisher information #Gaussian #Mathematics #Neural Networks and Applications #Physics #Quantum mechanics #Spatial correlation #Statistical Mechanics and Entropy #Statistical physics #Statistics #cond-mat.dis-nn #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.80.051125
published in Physical Review E 80(5), 051125 (American Physical Society) · 18 pages, 3 figures: revised version accepted in Phys. Rev. E
arxiv created 2009/10/31 · openalex publication_date 2009/11/24 · arxiv updated 2015/05/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 g_\ensuremathθn\ensuremathθm for (\ensuremathθ1,\ensuremathθ2,\ensuremathθ3)=(\ensuremathμq,\ensuremathσq2,s), where \ensuremathμq, \ensuremathσq2, and s denote the mean, variance, and degree of spatial correlation, respectively, for a given entropic index q. It has been shown from the Cram'er-Rao theorem that (1) an accuracy of an unbiased estimate of \ensuremathμq is improved (degraded) by a negative (positive) correlation s, (2) that of \ensuremathσq2 is worsen with increasing s, and (3) that of s is much improved for s\ensuremath≃\ensuremath-1/(N\ensuremath-1) or s\ensuremath≃1.0 though it is worst at s=(N\ensuremath-2)/2(N\ensuremath-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.