Statistical Inference
In the theory of statistical inference, the idea of a sufficient statistic provides the basis of choosing a statistic (as a function of the sample data points) in such a way that no information is lost by replacing the full probabilistic description of the sample with the sampling distribution of the selected statistic.
In frequentist inference, for example in the development of a statistical hypothesis test or a confidence interval, the availability of the sampling distribution of a statistic (or an approximation to this in the form of an asymptotic distribution) can allow the ready formulation of such procedures, whereas the development of procedures starting from the joint distribution of the sample would be less straightforward.
In Bayesian inference, when the sampling distribution of a statistic is available, one can consider replacing the final outcome of such procedures, specifically the conditional distributions of any unknown quantities given the sample data, by the conditional distributions of any unknown quantities given selected sample statistics. Such a procedure would involve the sampling distribution of the statistics. The results would be identical provided the statistics chosen are jointly sufficient statistics.
Read more about this topic: Sampling Distribution
Famous quotes containing the word inference:
“The inference is, that God has restated the superiority of the West. God always does like that when a thousand white people surround one dark one. Dark people are always “bad” when they do not admit the Divine Plan like that. A certain Javanese man who sticks up for Indonesian Independence is very lowdown by the papers, and suspected of being a Japanese puppet.”
—Zora Neale Hurston (1891–1960)