Table 3:

Comparison of BNN, GAM, random forest, and BART in variable selection and class prediction for the simulated classification example: “MPM” denotes the median probability model, i.e., selecting the variables with the marginal inclusion probability greater than 0.5; “Fitting” denotes the error rate of fitted class for the training data; “Prediction” denotes the error rate of predicted class for the test data; $\left|\overline{s_i^{*}}\right|$ denotes the average number of variables selected for the 10 datasets; the numbers in parentheses denote the standard deviations of the corresponding values; and p-value is calculated using a paired-t test for BNN versus every other method.

Methods	Setting	$\overline{\left|s_i^{*}\right|}$	fsr	nsr	Fitting(%)	Prediction(%)	p-value
BNN	MPM	4.3 (0.26)	0.093	0.025	3.57 (0.47)	9.70 (0.99)	—
GAM		13.5 (3.68)	0.73	0.10	12.13 (1.34)	15.57 (1.97)	2.75 × 10−3
	5 trees	17.3 (2.23)	0.79	0.075	2.19 (0.41)	18.6 (2.18)	7.45 × 10−4
RF	10 trees	8.2 (0.76)	0.56	0.10	0.67 (0.15)	17.2 (1.80)	2.98 × 10−3
	25 trees	5.2 (0.39)	0.31	0.10	0.0 (0.0)	14.3 (1.04)	1.27 × 10−3
	20 trees	2.8 (0.33)	0.0	0.30	9.90 (1.04)	17.72 (1.83)	2.01 × 10−4
BART	35 trees	3.0 (0.26)	0.0	0.25	6.83 (0.89)	17.00 (1.34)	3.35 × 10−6
	50 trees	3.0 (0.30)	0.0	0.25	5.33 (0.75)	15.57 (1.42)	7.46 × 10−4
	75 trees	3.3 (0.33)	0.03	0.20	4.47 (0.55)	16.90 (1.58)	2.22 × 10−4
SIS-SCAD		5.0 (1.45)	0.46	0.325	18.70 (2.91)	21.43 (2.48)	6.87 × 10–4