function update_linear_normal_inverse_gamma_gaussian(a:Real, x:Real, c:Real, μ:Real, a2:Real, α:Real, β:Real) -> (Real, Real, Real, Real)

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

  • a: Scale.
  • x: The variate.
  • c: Offset.
  • μ: Mean.
  • a2: Variance.
  • α: Shape of the inverse-gamma.
  • β: Scale of the inverse-gamma.

Returns: the updated parameters μ, a2, α and β.