  We consider generalizations of the classical inverse problem to Bayesien type
estimators, where the result is not one optimal parameter but an optimal
probability distribution in parameter space. The practical computational tool
to compute these distributions is the Metropolis Monte Carlo algorithm. We
derive kinetic theories for the Metropolis Monte Carlo method in different
scaling regimes. The derived equations yield a different point of view on the
classical algorithm. It further inspired modifications to exploit the
difference scalings shown on an simulation example of the Lorenz system.
