Uniformly Most Powerful Test - Setting

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 .

\phi(x) = \begin{cases} 1 & \text{if } x \in R \\ 0 & \text{if } x \in A \end{cases}

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

Famous quotes containing the word setting:

    “We don’t arrive at it by standing on one leg or on the first day of our setting out—but though we may jostle one another on the way that is no reason why we should strike or trample—elbowing’s enough.”
    —George Gordon Noel Byron (1788–1824)

    “The setting was really perfect for a brisk bubbling murder....”
    —Vladimir Nabokov (1899–1977)

    “Only in the problem play is there any real drama, because drama is no mere setting up of the camera to nature: it is the presentation in parable of the conflict between Man’s will and his environment: in a word, of problem.”
    —George Bernard Shaw (1856–1950)