  We introduce a general IFS Bayesian method for getting posterior
probabilities from prior probabilities, and also a generalized Bayes' rule,
which will contemplate a dynamical, as well as a non-dynamical setting. Given a
loss function ${l}$, we detail the prior and posterior items, their
consequences and exhibit several examples. Taking $\Theta$ as the set of
parameters and $Y$ as the set of data (which usually provides {random
samples}), a general IFS is a measurable map $\tau:\Theta\times Y \to Y$, which
can be interpreted as a family of maps $\tau_\theta:Y\to Y,\,\theta\in\Theta$.
The main inspiration for the results we will get here comes from a paper by
Zellner (with no dynamics), where Bayes' rule is related to a principle of
minimization of {information.} We will show that our IFS Bayesian method which
produces posterior probabilities (which are associated to holonomic
probabilities) is related to the optimal solution of a variational principle,
somehow corresponding to the pressure in Thermodynamic Formalism, and also to
the principle of minimization of information in Information Theory. Among other
results, we present the prior dynamical elements and we derive the
corresponding posterior elements via the Ruelle operator of Thermodynamic
Formalism; getting in this way a form of dynamical Bayes' rule.
