Mathematical Definition
A statistic T(X) is sufficient for underlying parameter θ precisely if the conditional probability distribution of the data X, given the statistic T(X), does not depend on the parameter θ, i.e.
or in shorthand
Read more about this topic: Sufficient Statistic
Famous quotes containing the words mathematical and/or definition:
“It is by a mathematical point only that we are wise, as the sailor or the fugitive slave keeps the polestar in his eye; but that is sufficient guidance for all our life. We may not arrive at our port within a calculable period, but we would preserve the true course.”
—Henry David Thoreau (1817–1862)
“Beauty, like all other qualities presented to human experience, is relative; and the definition of it becomes unmeaning and useless in proportion to its abstractness. To define beauty not in the most abstract, but in the most concrete terms possible, not to find a universal formula for it, but the formula which expresses most adequately this or that special manifestation of it, is the aim of the true student of aesthetics.”
—Walter Pater (1839–1894)