function update_linear_multivariate_gaussian_gaussian(x:Real, a:Real[_], μ:Real[_], Σ:LLT, c:Real, s2:Real) -> (Real[_], LLT)

Update the parameters of a multivariate Gaussian distribution with a linear transformation involving a dot product, and a multivariate Gaussian likelihood.

  • x: The variate.
  • a: Scale.
  • μ: Prior mean.
  • Σ: Prior covariance.
  • c: Offset.
  • s2: Likelihood covariance.

Returns: the posterior hyperparameters μ' and Σ'.