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Concept
Uniformly most powerful test
Summary
In statistical hypothesis testing, a uniformly most powerful (UMP) test is a hypothesis test which has the greatest power 1 - \beta among all possible tests of a given size α. For example, according to the Neyman–Pearson lemma, the likelihood-ratio test is UMP for testing simple (point) hypotheses.
Setting
Let X denote a random vector (corresponding to the measurements), taken from a parametrized family of probability density functions or probability mass functions f_{\theta}(x), which depends on the unknown deterministic parameter \theta \in \Theta. The parameter space \Theta is partitioned into two disjoint sets \Theta_0 and \Theta_1. Let H_0 denote the hypothesis that \theta \in \Theta_0, and let H_1 denote the hypothesis that \theta \in \Theta_1.
The binary test of hypotheses is performed using a test function \varphi(x)
Official source
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