Action-Space/Expected- Cost-of-Classification (ECC) Approach to Theoretical Seismic Discrimination: Undecided Regions Unequal Population Variances Costs and Benefits Prior Probability Outlier Analysis Three or More Populations Test Sites and Variation of Discrimination Threshold with Magnitude

摘要

Some procedures for discriminating between earthquakes (Q) and explosions (X) set aside a region of the discrimination parameter space (x) in which no decision is made; this may be called the 'unidentified' or 'undecided' region, (U). Tile existing statistical literature seems not to explicitly provide any such option, although an undecided region may be rigorously supported by the decision theory literature on 'action spaces.' In this report we show how the concept of U arises naturally from the concept of the costs of classification: positive costs from misclassifications and 'no decisions', and negative costs (benefits) from correct classifications. The resulting approach is a generalization of the 'Expected Cost of Misclassification' (ECM) approach; we call the generalization the 'Expected Cost of Classification' (ECC) approach. We also show how thresholds for detecting X as outliers of a Q population may be derived from cost considerations together with uniform distributions for X, and, together with plausible prior probabilities for Q and X, lead to reasonable thresholds in realistic scenarios.