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:
“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)
“Linnæus, setting out for Lapland, surveys his “comb” and “spare shirt,” “leathern breeches” and “gauze cap to keep off gnats,” with as much complacency as Bonaparte a park of artillery for the Russian campaign. The quiet bravery of the man is admirable.”
—Henry David Thoreau (1817–1862)
“In my dealing with my child, my Latin and Greek, my accomplishments and my money stead me nothing; but as much soul as I have avails. If I am wilful, he sets his will against mine, one for one, and leaves me, if I please, the degradation of beating him by my superiority of strength. But if I renounce my will, and act for the soul, setting that up as umpire between us two, out of his young eyes looks the same soul; he reveres and loves with me.”
—Ralph Waldo Emerson (1803–1882)