function downdate_linear_matrix_normal_inverse_wishart_matrix_gaussian(X:Real[_,_], A:Real[_,_], N':Real[_,_], Λ':LLT, C:Real[_,_], V':Real[_,_], k':Real) -> (Real[_,_], LLT, Real[_,_], Real)

Downdate the parameters of a Gaussian variate with linear transformation of matrix-normal-inverse-Wishart prior.

  • x: The variate.
  • A: Scale.
  • N': Posterior precision times mean matrix.
  • Λ': Posterior precision.
  • C: Offset.
  • V': Posterior variance shape.
  • k': Posterior degrees of freedom.

Returns: the prior hyperparameters N, Λ, V and k.