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
Famous quotes containing the word setting:
“When I consider the clouds stretched in stupendous masses across the sky, frowning with darkness or glowing with downy light, or gilded with the rays of the setting sun, like the battlements of a city in the heavens, their grandeur appears thrown away on the meanness of my employment; the drapery is altogether too rich for such poor acting. I am hardly worthy to be a suburban dweller outside those walls.”
—Henry David Thoreau (1817–1862)
“Dandyism is the last flicker of heroism in decadent ages.... Dandyism is a setting sun; like the declining star, it is magnificent, without heat and full of melancholy. But alas! the rising tide of democracy, which spreads everywhere and reduces everything to the same level, is daily carrying away these last champions of human pride, and submerging, in the waters of oblivion, the last traces of these remarkable myrmidons.”
—Charles Baudelaire (1821–1867)
“Teaching Black Studies, I find that students are quick to label a black person who has grown up in a predominantly white setting and attended similar schools as “not black enough.” ...Our concept of black experience has been too narrow and constricting.”
—bell hooks (b. c. 1955)