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

(a)我们将自由度的统计数（NDF）定义为二维随机场中每单位面积的等效不相关点数。(b)一阶NDF等于第一统计矩的费雪信息。二阶NDF近似于费雪关于二阶矩的信息。(c)从NDF推断出随机场和随机过程的许多有趣特征。它们是相关时间、相关长度、相关面积、线相关、区域相关和束相关。(d)两个随机过程之间的相互信息和矢量相关系数对于衡量它们如何在全球相互关联是有用的。从理论上和数值上研究了互信息与矢量相关的关系。(e)将上述结果应用于一些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.