A common alternative to evaluate and compare models in the Bayesian world (at least in some of its countries) are the Bayes factors.

One problem with Bayes factors is that their computation can be highly sensitive to aspects of the priors that have no practical effect on the posterior distribution of individual models. You may have noticed in previous examples that, in general, having a normal prior with a standard deviation of 100 is the same as having one with a standard deviation of 1,000, Instead, Bayes factors will be generally affected by these kind of changes in the model. Another problem with Bayes factors is that their computations can be more difficult than inference. One final criticism is that Bayes factors can be used as a Bayesian way of doing hypothesis testing; there is nothing wrong in this per se, but many authors have pointed out that an inference or modeling approach, similar to the one used in this book, is better suited to most problems than the generally...