  A novel formalism for Bayesian learning in the context of complex inference
models is proposed. The method is based on the use of the Stationary
Fokker--Planck (SFP) approach to sample from the posterior density. Stationary
Fokker--Planck sampling generalizes the Gibbs sampler algorithm for arbitrary
and unknown conditional densities. By the SFP procedure approximate analytical
expressions for the conditionals and marginals of the posterior can be
constructed. At each stage of SFP, the approximate conditionals are used to
define a Gibbs sampling process, which is convergent to the full joint
posterior. By the analytical marginals efficient learning methods in the
context of Artificial Neural Networks are outlined. Off--line and incremental
Bayesian inference and Maximum Likelihood Estimation from the posterior is
performed in classification and regression examples. A comparison of SFP with
other Monte Carlo strategies in the general problem of sampling from arbitrary
densities is also presented. It is shown that SFP is able to jump large
low--probabilty regions without the need of a careful tuning of any step size
parameter. In fact, the SFP method requires only a small set of meaningful
parameters which can be selected following clear, problem--independent
guidelines. The computation cost of SFP, measured in terms of loss function
evaluations, grows linearly with the given model's dimension.
