Following this, the predictive accuracy from various models can be compared using the Watanabe–Akaike information criterion (WAIC) (Vehtari and Gelman 2014; Watanabe 2010):\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathrm{WAIC}=-2\left(\widehat{lpd}-{\widehat{P}}_{\mathrm{waic}}\right) $$\end{document}WAIC=−2lpd^−P^waicwhere \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \widehat{lpd} $$\end{document}lpd^ represents the computed log pointwise predictive density and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\widehat{P}}_{\mathrm{waic}} $$\end{document}P^waic is the estimated effective number of parameters (Vehtari and Gelman 2014; Watanabe 2010). The model with the lowest WAIC is selected to achieve a trade-off between model complexities. WAIC was derived based on a singular learning theory as an asymptotically unbiased approximation to the out-of-sample prediction error and is a generalization of Akaike’s information criterion that is applicable to both regular and singular statistical models (Watanabe 2010). The variable selection in the Bayesian linear regression modeling was evaluated based on the stepwise forward selection method by WAIC.