function update_multivariate_normal_inverse_gamma(x:Real[_], ν:Real[_], Λ:LLT, α:Real, β:Real) -> (Real, Real)

Update the parameters of an inverse-gamma distribution with a linear scaling and Gaussian likelihood.

  • x: The variate.
  • ν: Precision times mean.
  • Λ: Precision.
  • α: Prior shape of the inverse-gamma.
  • β: Prior scale of the inverse-gamma.

Returns: the posterior hyperparameters α' and β'.