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Most geological phenomena are multivariate in nature; for example, a porous medium is characterized by a set of interdependent quantities or attributes such as grain size, [[porosity]], [[permeability]], and saturation. Although univariate statistical analysis can characterize the distribution of each attribute separately, an understanding of porous media calls for unraveling the interrelationships among their various attributes. Multivariate statistical analysis proposes to study the joint distribution of all attributes, in which the distribution of any single variable is analyzed as a function of the other attributes distributions.

Most geological phenomena are multivariate in nature; for example, a porous medium is characterized by a set of interdependent quantities or attributes such as [[grain size]], [[porosity]], [[permeability]], and saturation. Although univariate statistical analysis can characterize the distribution of each attribute separately, an understanding of porous media calls for unraveling the interrelationships among their various attributes. Multivariate statistical analysis proposes to study the joint distribution of all attributes, in which the distribution of any single variable is analyzed as a function of the other attributes distributions.

Multivariate observations are best organized and manipulated as a matrix of sample values, of size (n × P), where n is the number of samples and P is the number of attributes or variables. For example, a (5 × 3) matrix might represent five core samples at different depths on which frequencies of occurrence of three different fossils are recorded. The purposes of multivariate data analysis is to study the relationships among the P attributes, classify the n collected samples into homogeneous groups, and make inferences about the underlying populations from the sample.

Multivariate observations are best organized and manipulated as a matrix of sample values, of size (n × P), where n is the number of samples and P is the number of attributes or variables. For example, a (5 × 3) matrix might represent five core samples at different depths on which frequencies of occurrence of three different fossils are recorded. The purposes of multivariate data analysis is to study the relationships among the P attributes, classify the n collected samples into homogeneous groups, and make inferences about the underlying populations from the sample.