function downdate_normal_inverse_gamma_gaussian(x:Real, μ':Real, λ':Real, α':Real, β':Real) -> (Real, Real, Real, Real)

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

  • x: The variate.
  • μ': Posterior mean.
  • λ': Posterior precision.
  • α': Posterior shape of the inverse-gamma.
  • β': Posterior scale of the inverse-gamma.

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