Hasegawa Hideo
Department of Physics, Tokyo Gakugei University, Koganei, Tokyo 184-8501, Japan.
Phys Rev E Stat Nonlin Soft Matter Phys. 2008 Aug;78(2 Pt 1):021141. doi: 10.1103/PhysRevE.78.021141. Epub 2008 Aug 28.
We have calculated the Tsallis entropy and Fisher information matrix (entropy) of spatially correlated nonextensive systems, by using an analytic non-Gaussian distribution obtained by the maximum entropy method. The effects of the correlated variability on the Fisher information matrix are shown to be different from those on the Tsallis entropy. The Fisher information is increased (decreased) by a positive (negative) correlation, whereas the Tsallis entropy is decreased with increasing absolute magnitude of the correlation, independently of its sign. This fact arises from the difference in their characteristics. It implies from the Cramér-Rao inequality that the accuracy of an unbiased estimate of fluctuation is improved by a negative correlation. A critical comparison is made between the present study and previous ones employing the Gaussian approximation for the correlated variability due to multiplicative noise.
我们通过使用最大熵方法得到的解析非高斯分布，计算了空间相关非广延系统的Tsallis熵和Fisher信息矩阵（熵）。结果表明，相关变异性对Fisher信息矩阵的影响与对Tsallis熵的影响不同。正（负）相关会使Fisher信息增加（减少），而Tsallis熵则随着相关绝对值的增加而减小，与相关的符号无关。这一事实源于它们特性的差异。根据克拉美-罗不等式，这意味着负相关会提高涨落无偏估计的精度。本研究与之前采用高斯近似处理乘性噪声引起的相关变异性的研究进行了关键比较。
