24.2 Inverse Wishart Distribution
24.2.1 Probability Density Function
If \(K \in \mathbb{N}\), \(\nu \in (K-1,\infty)\), and \(S \in \mathbb{R}^{K \times K}\) is symmetric and positive definite, then for symmetric and positive-definite \(W \in \mathbb{R}^{K \times K}\), \[ \text{InvWishart}(W|\nu,S) = \frac{1}{2^{\nu K / 2}} \ \frac{1}{\Gamma_K \! \left( \frac{\nu}{2} \right)} \ \left| S \right|^{\nu/2} \ \left| W \right|^{-(\nu + K + 1)/2} \ \exp \! \left( - \frac{1}{2} \ \text{tr}(SW^{-1}) \right) \! . \]
24.2.2 Sampling Statement
W ~ inv_wishart(nu, Sigma)
Increment target log probability density with inv_wishart_lpdf(W | nu, Sigma)
dropping constant additive terms.
24.2.3 Stan Functions
real inv_wishart_lpdf(matrix W | real nu, matrix Sigma)
The log of the inverse Wishart density for symmetric and
positive-definite matrix W given degrees of freedom nu and symmetric
and positive-definite scale matrix Sigma
matrix inv_wishart_rng(real nu, matrix Sigma)
Generate an inverse Wishart variate with degrees of freedom nu and
symmetric and positive-definite scale matrix Sigma; may only be used
in transformed data and generated quantities blocks