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:

    “The world is ... the natural setting of, and field for, all my thoughts and all my explicit perceptions. Truth does not “inhabit” only “the inner man,” or more accurately, there is no inner man, man is in the world, and only in the world does he know himself.”
    —Maurice Merleau-Ponty (1907–1961)

    “it is finally as though that thing of monstrous interest
    were happening in the sky
    but the sun is setting and prevents you from seeing it”
    —John Ashbery (b. 1927)

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