function downdate_linear_matrix_normal_inverse_gamma_matrix_gaussian(X:Real[_,_], A:Real[_,_], N':Real[_,_], Λ':LLT, C:Real[_,_], α':Real, γ':Real[_]) -> (Real[_,_], LLT, Real, Real[_])

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

  • x: The variate.
  • A: Scale.
  • N': Posterior precision times mean matrix.
  • Λ': Posterior precision.
  • C: Offset.
  • α': Posterior variance shape.
  • γ': Posterior squared sum accumulators.

Returns: the prioor hyperparameters N, Λ, α and γ.