Downdate multivariate linear gaussian gaussian

function downdate_multivariate_linear_gaussian_gaussian(x:Real[_], A:Real[_,_], μ':Real[_], Σ':Real[_,_], c:Real[_], S:Real[_,_]) -> (Real[_], Real[_,_])

Downdate the parameters of a multivariate Gaussian distribution with a multivariate Gaussian likelihood and scaling.

  • x: The variate.
  • A: Scale.
  • μ': Posterior mean.
  • Σ': Posterior covariance.
  • c: Offset.
  • S: Likelihood covariance.

Returns: the prior hyperparameters μ and Σ.