Setting
Let denote a random vector (corresponding to the measurements), taken from a parametrized family of probability density functions or probability mass functions, which depends on the unknown deterministic parameter . The parameter space is partitioned into two disjoint sets and . Let denote the hypothesis that, and let denote the hypothesis that . The binary test of hypotheses is performed using a test function .
meaning that is in force if the measurement and that is in force if the measurement . Note that is a disjoint covering of the measurement space.
Read more about this topic: Uniformly Most Powerful Test
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