This paper reviews the Akaike (AIC), Deviance Information Criterion (DIC), and Watanabe-Akaike Information Criterion (WAIC) information criteria from a Bayesian perspective, focusing on their use in estimating out-of-sample prediction error. The authors compare these criteria in three examples, one theoretical and two applied, to better understand their practical applications. They emphasize the importance of bias correction when estimating predictive accuracy, as models are often evaluated on data used to fit them. Cross-validation is a natural method for estimating out-of-sample prediction error, but it can be computationally intensive and may not be feasible with sparse data. As alternatives, AIC, DIC, and WAIC are considered, with WAIC being the most Bayesian and preferred for its ability to account for model complexity. The paper also discusses the effective number of parameters in these criteria, noting that they differ in how they adjust for model complexity. The authors conclude that WAIC is more accurate than AIC and DIC in many cases, and that cross-validation provides a more direct estimate of predictive accuracy, though it can be computationally expensive. The paper highlights the importance of understanding these criteria in the context of Bayesian model comparison and prediction.This paper reviews the Akaike (AIC), Deviance Information Criterion (DIC), and Watanabe-Akaike Information Criterion (WAIC) information criteria from a Bayesian perspective, focusing on their use in estimating out-of-sample prediction error. The authors compare these criteria in three examples, one theoretical and two applied, to better understand their practical applications. They emphasize the importance of bias correction when estimating predictive accuracy, as models are often evaluated on data used to fit them. Cross-validation is a natural method for estimating out-of-sample prediction error, but it can be computationally intensive and may not be feasible with sparse data. As alternatives, AIC, DIC, and WAIC are considered, with WAIC being the most Bayesian and preferred for its ability to account for model complexity. The paper also discusses the effective number of parameters in these criteria, noting that they differ in how they adjust for model complexity. The authors conclude that WAIC is more accurate than AIC and DIC in many cases, and that cross-validation provides a more direct estimate of predictive accuracy, though it can be computationally expensive. The paper highlights the importance of understanding these criteria in the context of Bayesian model comparison and prediction.