28.3 Inverse Wishart distribution
28.3.1 Probability density function
If K∈N, ν∈(K−1,∞), and S∈RK×K is symmetric and positive definite, then for symmetric and positive-definite W∈RK×K, InvWishart(W∣ν,S)=12νK/2 1ΓK(ν2) |S|ν/2 |W|−(ν+K+1)/2 exp(−12 tr(SW−1)).
28.3.2 Sampling statement
W ~
inv_wishart
(nu, Sigma)
Increment target log probability density with inv_wishart_lupdf(W | nu, Sigma)
.
Available since 2.0
28.3.3 Stan functions
real
inv_wishart_lpdf
(matrix W | real nu, matrix Sigma)
Return 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
.
Available since 2.12
real
inv_wishart_lupdf
(matrix W | real nu, matrix Sigma)
Return 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
dropping constant additive terms.
Available since 2.25
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.
Available since 2.0