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28.3 Inverse Wishart distribution

28.3.1 Probability density function

If KN, ν(K1,), and SRK×K is symmetric and positive definite, then for symmetric and positive-definite WRK×K, InvWishart(Wν,S)=12νK/2 1ΓK(ν2) |S|ν/2 |W|(ν+K+1)/2 exp(12 tr(SW1)).

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