Table 1:

True positive rates (TPR) and true negative rates (TNR) for Gaussian synthetic data with $p^{\text{*}}+1=6$ active covariates including the intercept. The selection performance of ${𝒮}_{\mathit{\text{small}}}$ is excellent and similar to the the adaptive lasso. Classical subset, forward, and backward selection are too aggressive, while the posterior interval-based selection is too conservative.

$n=50$, $p=50$, SNR = 0.25
	lasso	forward	backward	subset	posterior HPD	$S_{min}$	$S_{\mathit{\text{small}}}$
TPR	0.22	0.96	0.93	0.53	0.06	0.51	0.22
TNR	0.98	0.06	0.10	0.63	1.00	0.81	0.98
$n=50$, $p=50$, SNR = 1
	lasso	forward	backward	subset	posterior HPD	$S_{min}$	$S_{\mathit{\text{small}}}$
TPR	0.54	0.95	0.89	0.72	0.16	0.77	0.34
TNR	0.92	0.06	0.11	0.64	1.00	0.78	0.99
$n=200$, $p=400$, SNR = 0.25
	lasso	forward	backward	subset	posterior HPD	$S_{min}$	$S_{\mathit{\text{small}}}$
TPR	0.36	0.79	0.78	0.67	0.17	0.75	0.34
TNR	1.00	0.52	0.54	0.96	1.00	0.95	1.00
$n=200$, $p=400$, SNR = 1
	lasso	forward	backward	subset	posterior HPD	$S_{min}$	$S_{\mathit{\text{small}}}$
TPR	0.97	0.96	0.95	0.95	0.75	0.98	0.93
TNR	0.99	0.57	0.60	0.96	1.00	0.95	1.00
$n=500$, $p=50$, SNR = 0.25
	lasso	forward	backward	subset	posterior HPD	$S_{min}$	$S_{\mathit{\text{small}}}$
TPR	0.84	0.96	0.95	0.94	0.59	0.99	0.86
TNR	0.98	0.83	0.83	0.83	1.00	0.70	0.98
$n=500$, $p=50$, SNR = 1
	lasso	forward	backward	subset	posterior HPD	$S_{min}$	$S_{\mathit{\text{small}}}$
TPR	1.00	1.00	1.00	1.00	1.00	1.00	1.00
TNR	1.00	0.84	0.83	0.83	1.00	0.67	0.99