GLOBAL CORRELATION METHODS FOR FEATURING A RANDOM FIELD AND A MULTIDIMENSIONAL MULTIVARIATE TIME SERIES AND THEIR APPLICATIONS

(A)我们将统计自由度数(NDF)定义为在二维随机场中单位面积上的等价不相关点数。(B)一阶NDF等于Fisher关于一阶统计矩的信息。二阶NDF是关于二阶矩的Fisher信息的近似。(C)从NDF可以推导出随机场和随机过程的许多有趣的特征，它们是相关时间、相关长度、相关面积、线相关、面积相关和束相关。(D)两个随机过程之间的互信息和向量相关系数有助于衡量它们是如何全局相关的。从理论和数值两个方面研究了互信息与向量相关之间的关系。(E)将上述结果应用于气象数据和生物医学数据的年化。

(a)We defined statistical numbers of degrees of freedom (NDF) as an equivalent uncorrelated number of points per unit area in a 2-dimensional random field.(b)The first order NDF is equal to Fisher's information about the first statistical moment. The second order NDF is an approximation of Fisher's information about the second moment.(c)Many interesting features of a random field and a random process were deduced from the NDF's. They are correlation time, correlation length, correlation area, line-correlation, area-correlation, and bundle-correlation.(d)The mutual information and the vector correlation coefficient between two random processes are useful to measure how they are globally correlated. Relationship between mutual information and vector correlation were investigated both theoretically and numerically.(e)The results obtalned above were applied to annualizing some meteorological data and biomedical data.