Table 1:

Comparison of BNN, GAM, random forest, and BART in variable selection and nonlinear prediction for the simulated nonlinear regression example: “MPM” denotes the median probability model, i.e., selecting only the variables with the marginal inclusion probability greater than 0.5; “MSFE” denotes the mean squared fitting error; “MSPE” denotes the mean squared prediction error for the mean response; $\overline{\left|s_i^{*}\right|}$ denotes the average number of variables selected for the 10 datasets; the numbers in parentheses denote the standard deviations of the corresponding values;

Methods	Setting	$\overline{\left|s_i^{*}\right|}$	fsr	nsr	MSFE	MSPE
BNN	MPM	5.2 (0.13)	0.038	0	1.53(0.09)	2.03(0.20)
BRNN		195.9+ (0.09)	0.667	0.60	0.013(9.9×10−4)	19.51(0.82)
GAM		41.3 (6.77)	0.898	0.16	3.78 (0.37)	6.09 (0.29)
RF		7.1 (0.43)	0.76	0.66	1.83 (0.05)	9.71 (0.34)
	20 trees	5.9 (2.87)	0.64	0.58	2.79 (0.17)	8.45 (0.34)
BART	35 trees	8.0 (4.34)	0.75	0.60	1.54 (0.09)	8.57 (0.42)
	50 trees	4.3 (2.53)	0.56	0.62	0.82 (0.07)	8.34 (0.38)
SIS-SCAD		12.4 (5.37)	0.83	0.58	5.79 (0.81)	9.32 (0.91)

⁺BRNN reports the effective number of parameters instead of the number of selected variables.