While simple in concept, this method is necessarily crude and limited. In addition, this method does not allow us to obtain a confidence range on the best model. The resulting posterior probability distribution completely characterizes our state of knowledge about the model parameters in question. Naturally, this is of limited use unless a means for estimating the reliability of the MAP solution is also available. A model may have many parameters in which we are not interested, or are simply not known with sufficient knowledge.
Bayesian theory is able to handle such cases unlike frequency statitsics.
This is especially true of Decision theoretic analyses. This method is used in cases where the prior information is not enough to solve the problem, but constrains on the final solution do exist. Note that the concept of entropy as used here is not the physical quantity of statistical physics, though the two are mathematically similar. In highly complicated systems, calculating posteriors that involve non-standard likelihoods and priors may be computationally intractable. In such cases, simulated random initial states of model parameters may be used to generate final states through a series of applications of Bayes' theorem such that each succeeding state depends only on the previous state.