Figure 2. The mean-field/Laplace approximation.

The variational Bayesian approach furnishes an approximation to the marginal posterior densities of subsets of unknown model parameters . Here, the 2D landscape depicts a (true) joint posterior density and the two black lines are the subsequent marginal posterior densities of and , respectively. The mean-field approximation basically describes the joint posterior density as the product of the two marginal densities (black profiles). In turn, stochastic dependencies between parameter subsets are replaced by deterministic dependencies between their posterior sufficient statistics. The Laplace approximation further assumes that the marginal densities can be described by Gaussian densities (red profiles).