Downdate multivariate dot normal inverse gamma gaussian

function downdate_multivariate_dot_normal_inverse_gamma_gaussian(x:Real, a:Real[_], ν':Real[_], c:Real, Λ':LLT, γ':Real, α':Real, β':Real) -> (Real[_], LLT, Real, Real, Real)

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

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

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