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 . |