Another common Information Criterion is Deviance Information Criterion (DIC). If we use the bayes-o-meter™ , this is somehow in the middle between AIC and WAIC. While still popular, WAIC has been proved more useful both theoretically and empirically than DIC, and thus using WAIC is recommended over DIC.

Yet another information criteria is the Bayesian Information Criterion (BIC), which is similar to logistic regression and my mother's sopa seca. This name can be misleading. BIC was proposed as a way to correct some of the problems with AIC, and the author proposed a Bayesian justification for it. But BIC is not really Bayesian, and in fact is pretty similar to AIC. It also assumes flat priors and uses a maximum likelihood estimate. Even more importantly, BIC is different to AIC and WAIC and is more related to the concept of Bayes factors, something we will discuss later in this chapter.