The article reviews the Akaike Information Criterion (AIC), Deviance Information Criterion (DIC), and Watanabe-Akaike Information Criterion (WAIC) from a Bayesian perspective, focusing on estimating expected out-of-sample prediction error using a bias-corrected adjustment of within-sample error. The authors compare these criteria in three examples, one theoretical and two applied, to understand how they can be applied in practice. They emphasize the importance of understanding the Bayesian predictive context and the choices involved in setting up these measures. The article discusses the limitations of cross-validation and the advantages of bias corrections like AIC, DIC, and WAIC. It also explores the concept of log predictive density as a measure of model accuracy and the role of effective number of parameters in these criteria. The authors provide theoretical and practical examples to illustrate the differences between AIC, DIC, and WAIC, highlighting WAIC's advantages in handling singular models and hierarchical structures.The article reviews the Akaike Information Criterion (AIC), Deviance Information Criterion (DIC), and Watanabe-Akaike Information Criterion (WAIC) from a Bayesian perspective, focusing on estimating expected out-of-sample prediction error using a bias-corrected adjustment of within-sample error. The authors compare these criteria in three examples, one theoretical and two applied, to understand how they can be applied in practice. They emphasize the importance of understanding the Bayesian predictive context and the choices involved in setting up these measures. The article discusses the limitations of cross-validation and the advantages of bias corrections like AIC, DIC, and WAIC. It also explores the concept of log predictive density as a measure of model accuracy and the role of effective number of parameters in these criteria. The authors provide theoretical and practical examples to illustrate the differences between AIC, DIC, and WAIC, highlighting WAIC's advantages in handling singular models and hierarchical structures.