function downdate_multivariate_dot_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 univariate 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.