function update_linear_normal_inverse_gamma_gaussian(x:Real, a:Real, μ:Real, λ:Real, c:Real, α:Real, β:Real) -> (Real, Real, Real, Real)

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

  • x: The variate.
  • a: Scale.
  • μ: Prior mean.
  • λ: Prior precision.
  • c: Offset.
  • α: Prior shape of the inverse-gamma.
  • β: Prior scale of the inverse-gamma.

Returns: the posterior hyperparameters μ', λ', α' and β'.