function downdate_multivariate_linear_normal_inverse_gamma_gaussian(x:Real[_], A:Real[_,_], μ':Real[_], c:Real[_], Λ':Real[_,_], α':Real, β':Real) -> (Real[_], Real[_,_], Real, Real)

Downdate the parameters of a normal inverse-gamma distribution with a multivariate Gaussian likelihood and scaling.

  • x: The variate.
  • A: Scale.
  • μ': Posterior mean.
  • c: Offset.
  • Λ': Posterior precision.
  • α': Posterior shape of the inverse-gamma.
  • β': Posterior scale of the inverse-gamma.

Returns: the prior hyperparameters μ, Σ, α and β.