Fig 3. Effect of the parameters of a Gaussian prior on the performance of WAIC and LOO in selecting the epileptogenicity hypothesis for the 2D Epileptor model.

To illustrate how fully Bayesian information criteria are affected by the parameters of a Gaussian prior placed on the excitability parameter, Delta scores for WAIC and LOO are computed as a function of the mean and the standard deviation of prior. Panels (A) and (B) show the computed ΔWAIC and ΔLOO, respectively, when the prior placed on excitability parameter is a Gaussian distribution $\mathcal{N}(\mu ,{\sigma }^2)$, in which excitability value (denoted by μ) varies from -4.5 to 1.5, whereas the uncertainty about the estimation (denoted by σ) ranges from 0.01 to 1000. It can be seen that WAIC closely approximates LOO cross-validation. The figure plots the averages over 4 HMC chains. The dashed white line indicates the true value of excitability parameter used in the simulation. A larger value of WAIC/LOO indicates that the parameter is less plausible.