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 mind cannot support moral chaos for long. Men are under as strong a compulsion to invent an ethical setting for their behavior as spiders are to weave themselves webs.”
    —John Dos Passos (1896–1970)

    “should some limb of the devil
    Destroy the view by cutting down an ash
    That shades the road, or setting up a cottage
    Planned in a government office, shorten his life,
    Manacle his soul upon the Red Sea bottom.”
    —William Butler Yeats (1865–1939)

    “May we two stand,
    When we are dead, beyond the setting suns,
    A little from other shades apart,
    With mingling hair, and play upon one lute.”
    —William Butler Yeats (1865–1939)