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Table 1 Four Tasks of Integrative Hypothesis Tests

From: Bi-linear matrix-variate analyses, integrative hypothesis tests, and case-control studies

Tasks Description
Task A (modelling) estimate θ ω such that q(x|θ ω ) models the corresponding population of samples, with the performance evaluated by its corresponding ε A , e.g., the average error or generalisation error.
Task B (comparison) develop a statistics s based on the resulted models to test H 0 by Equation (22), with the performance evaluated by its corresponding ε B that measures the difference between two populations, e.g., the p-value.
Task C (classification) classify each sample to either ω=1 or 0, with the performance evaluated by its corresponding ε C , e.g., either the rate of incorrect classification by Equation (44) or alternatively the corresponding p-value obtained by a test based on a statistics by Equation (47).
Task D (assurance) test whether a reliable separating boundary exists between the two populations of samples, with the performance evaluated by its corresponding ε D .