Figure 2.

A heuristic illustration of Bayesian inference in terms of a likelihood distribution, a prior distribution and the resulting posterior distribution. All these distributions are functions of some hidden state or cause of observed data, where the likelihood and prior distributions constitute a generative model. The important issue to observe here is that as the precision (certainty) of the prior increases, it draws the posterior estimate towards it; and away from the likelihood distribution. Here, precision corresponds to the inverse variance or dispersion (width) of the distributions, indicated with the blue arrows. Under models with additive Gaussian noise, the precision of the likelihood corresponds to the inverse amplitude of the noise (the signal-to-noise ratio).