function downdate_linear_multivariate_normal_inverse_gamma_multivariate_gaussian(x:Real[_], A:Real[_,_], ν':Real[_], Λ':LLT, c:Real[_], α':Real, γ':Real) -> (Real[_], LLT, Real, Real)

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

  • x: The variate.
  • A: Scale.
  • ν': Posterior precision times mean.
  • Λ': Posterior precision.
  • c: Offset.
  • α': Posterior shape of the inverse-gamma.
  • γ': Posterior scale accumulator.

Returns: the prior hyperparameters μ, Λ, α, and γ.