LPPD stands for log point-wise predictive density

  • inference is based on each data point
marginal likelihood

WAIC

  • makes no assumption about the shape of the posterior (aic makes normality assumption on the posterior distribution)
  • Approximate on out of sample deviance
  • Converge to loocv
  • Log posterior predictive density + penalty proportional to the variance in the posterior predictions (larger number of parameters -> bigger variance)
  • guess the out-of-sample K-L Divergence