In statistics, a sufficient statistic is a statistic which has the property of sufficiency with respect to a statistical model and its associated unknown parameter, meaning that "no other statistic which can be calculated from the same sample provides any additional information as to the value of the parameter". A statistic is sufficient for a family of probability distributions if the sample from which it is calculated gives no additional information than does the statistic, as to which of those probability distributions is that of the population from which the sample was taken.

In practical terms, given a set Failed to parse (Missing texvc executable; please see math/README to configure.): \mathbf{X}

, a sufficient statistic is a function Failed to parse (Missing texvc executable; please see math/README to configure.): T(\mathbf{X})

, the joint distribution can be written as Failed to parse (Missing texvc executable; please see math/README to configure.): p(\mathbf{X}) = h(\mathbf{X}) \, g(\theta, T(\mathbf{X}))\, . From this factorization, it can easily be seen that the maximum likelihood estimate of Failed to parse (Missing texvc executable; please see math/README to configure.): \theta