Consider a dataset \(y=(y_1,\dots,y_n)\), \(p(y|\theta)\) the likelihood of a parametric model with parameter \(\theta\), and \((\theta^{(1)},\dots,\theta^{(S)})\) a sample from the posterior distribution \(p(\theta|y)\).
Define $$\textnormal{llpd} = \sum_{i=1}^n \log\left(\sum_{i=1}^Sp(y_i|\theta^{(s)}\right)$$ and $$p_\textnormal{WAIC} = \sum_{i=1}^n Var_{\theta|y}(\log p(y_i|\theta)).$$
Then the Widely Applicable Information Criteria is defined as $$WAIC = -2\textnormal{llpd} + 2p_\textnormal{WAIC}.$$ Models with a smaller WAIC are favored.