Updating of Population Parameters and Credibility of Discriminant Analysis

The uncertainty of classification in discriminant analysis may result from the original characteristics of the phenomena studied, the approach of inferring population parameters, and the credibility of the parameters which are estimated by geologist or statistician. A credibility function and a significance function are proposed. Both can be used to appraise the uncertainty of classification. The former is involved with the uncertainty resulting from the errors in the reward-penalty matrix, while the latter may be involved with the uncertainty resulting from the original characteristics of the phenomena studied and the statistical approach. Inappropriate classified results may be originated from the bias estimates of population parameters (mean vector and covariance matrix), which are estimated by bias samples. These bias estimates can be updated by constraining the varying region of the mean vector. The equations for updating Bayesian estimates of the mean vector and the covariance matrix are demonstrated if the mean vector is restricted to a subregion of the entire real space. Results for a gas reservoir indicate that the discriminant rules based on the updated equations are more efficient than the traditional discriminant rules.