Update multivariate dot normal inverse gamma gaussian

function update_multivariate_dot_normal_inverse_gamma_gaussian(x:Real, a:Real[_], ν:Real[_], c:Real, Λ:LLT, γ:Real, α:Real, β:Real) -> (Real[_], LLT, Real, Real, Real)

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

  • x: The variate.
  • a: Scale.
  • ν: Prior precision times mean.
  • c: Offset.
  • Λ: Prior precision.
  • γ: Prior scale accumulator.
  • α: Prior shape of the inverse-gamma.
  • β: Prior scale of the inverse-gamma.

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