In probability theory and statistics, the normal-Wishart distribution (or Gaussian-Wishart distribution) is a multivariate four-parameter family of continuous probability distributions.

It is the conjugate prior of a multivariate normal distribution with unknown mean and precision matrix (the inverse of the covariance matrix).

[1] Suppose has a multivariate normal distribution with mean

, where has a Wishart distribution.

has a normal-Wishart distribution, denoted as By construction, the marginal distribution over

is a multivariate normal distribution.

The marginal distribution over

, the posterior distribution of the parameters is where Generation of random variates is straightforward: