Related information measures for the associations of earth-science variables

A basic task in earth-science data integration is to quantify variable associations. Although manv measures have been used to determine the associations between quantitative variables, the ability to quantify qualitative attributes (e.g., categorical) is limited. Moreover, most traditional association measures are restricted to linear correlations or similarities, for example, correlation coefficient. The measures proposed in this report are designed on the basis of Shannon's entropy concepts, including directional related information, ordinary related information, and partial related information. The directional related information quantifies the association of one variable in terms of another. The ordinary related information determines the mutual association of two variables. The partial related information characterizes the association of an individual stale of one variable in terms of another variable. The properties of these measures are discussed and their sample estimates are derived from both maximum likelihood and Bayesian methods. The relations between these measures are illustrated by using synthetic examples. Two applications of these measures also are developed, including the selection of variables and evaluation of mineral resources. Finally, a case study is given to demonstrate the use of the measures in mineral resources evaluation.