Table 1. Summary of epileptogenicity hypothesis testing using the classical and Bayesian information criteria (BIC/AIC/WAIC/LOO) in terms of deviance (-2 times log predictive density), penalty term, and Delta scores.

Here, three hypotheses as EZ, PZ, and HZ are evaluated on the excitability parameter of a selected brain region, where the ground truth is EZ. The smaller deviance and penalty terms, the smaller the value of information criterion, the better the model’s predictive ability. The correct hypothesis has a Delta score of zero.

		Hypothesis
		EZ	PZ	HZ
BIC	$-2logp(y\mid {\widehat{\theta }}_{mle})$	6435.83± 2.08	6437.77 ± 1.48	6438.70 ± 2.42
	k (number of model parameters)	255	255	255
	n (number of data points)	10080	10080	10080
	${\text{BIC}}_{\mathrm{i}}=-2log\mathrm{p}(\mathrm{y}\mid {\widehat{\theta }}_{\text{mle}})+\mathrm{k}log\left(\mathrm{n}\right)$	8786.49 ± 2.08	8788.44 ± 1.48	8789.37 ± 2.42
	ΔBICi = BICi − BICmin	0.0	1.94	2.88
AIC	$-2logp(y\mid {\widehat{\theta }}_{mle})$	6435.83 ± 2.08	6437.774 ± 1.48	6438.70 ± 2.42
	k (number of model parameters)	255	255	255
	${\text{AIC}}_{\mathrm{i}}=-2log\mathrm{p}(\mathrm{y}\mid {\widehat{\theta }}_{\text{mle}})+2\mathrm{k}$	6945.83 ± 2.08	6947.77± 1.48	6948.70 ± 2.42
	ΔAICi = AICi − AICmin	0.0	1.94	2.88
WAIC (Uninformative prior)	−2lppdwaic	18053.88 ± 124.71	18071.15 ± 29.49	18140.93± 125.51
	peff	3309.14 ± 277.61	3481.87 ± 431.05	3478.11 ± 501.51
	WAICi = 2(lppdwaic − peff)	24672.17 ± 614.68	25034.89 ± 890.64	25097.17 ± 1109.20
	ΔWAICi = WAICi − WAICmin	0.0	362.73	425.00
LOO (Uninformative prior)	−2lppdloo	23693.80 ± 674.08	24036.58± 778.03	24143.98 ± 1136.79
	LOOi = −2lppdloo	23693.80 ± 674.08	24036.58± 778.03	24143.98 ± 1136.79
	ΔLOOi = LOOi − LOOmin	0.0	342.78	450.18
WAIC (Informative prior)	−2lppdwaic	18051.38 ± 108.21	19477.37 ± 297.94	20958.32 ± 289.23
	peff	3353.22 ± 236.12	4063.06 ± 86.26	4312.69 ± 64.99
	WAICi = −2(lppdwaic − peff)	24757.83 ± 557.47	27603.50 ± 461.54	29583.71 ± 329.20
	ΔWAICi = WAICi − WAICmin	0.0	2845.67	4825.88
LOO (Informative prior)	−2lppdloo	23759.25 ± 332.94	27177.02 ± 609.29	29962.104 ± 343.11
	LOOi = −2lppdloo	23759.25 ± 332.94	27177.02 ± 609.29	29962.104 ± 343.11
	ΔLOOi = LOOi − LOOmin	0.0	3417.78	6202.85