It is worth pointing out that the Graduate Learning Algorithm can also be seen from this perspective.
an examination of the GLa shows that when the plasticity term is fixed, parameters found by GLa also form a Markov chain G (t)  assuming the model is identifiable, it seems possible to use GLa in the same way as the MCMC methods: rather than forcing it to stop, we can run GLa until it reaches stationary distribution, if it exists.