Table 2.

Estimated posterior means and results for empirical simulation

	Case 1	Case 2	Case 3
N	10	5	3
μ1	-0.170 (0.037)	-0.169 (0.041)	-0.157 (0.041)
$${\sigma }_0^2$$	3.653×10-4	3.604×10-4	3.83×10-4
	(3×10-5)	(4.421×10-5)	(6.090×10-5)
$${\sigma }_1^2$$	0.984 (0.104)	0.968 (0.115)	0.955 (0.110)
Π1	0.151 (0.004)	0.153 (0.005)	0.156 (0.006)
$$\mathit{\text{cor}}{({\chi }_g,\widehat{{\chi }_g})}^{\ast }$$	0.972 (0.006)	0.993 (0.003)	0.953 (0.011)
FDR	0.030 (0.008)	0.046 (0.011)	0.068 (0.013)
$$\widehat{\mathit{\text{FDR}}}$$	0.024 (0.004)	0.037 (0.005)	0.049 (0.006)
Sensitivity	0.928 (0.014)	0.866 (0.020)	0.802 (0.025)
Specificity	0.995 (0.001)	0.994 (0.002)	0.991 (0.002)
	Case 4	Case 5	Case 6
N	10	5	3
μ1	0.007 (0.035)	0.006 (0.038)	-0.002 (0.037)
$${\sigma }_0^2$$	3.634×10-4	3.532×10-4	3.450×10-4
	(2.931×10-5)	(4.155×10-5)	(5.283×10-5)
$${\sigma }_1^2$$	1.172 (0.048)	1.151 (0.059)	1.140 (0.050)
Π1	0.179 (0.003)	0.183 (0.004)	0.188 (0.005)
$$\mathit{\text{cor}}{({\chi }_g,\widehat{{\chi }_g})}^{\ast }$$	0.990 (0.002)	0.979 (0.004)	0.965 (0.007)
FDR	0.030 (0.008)	0.044 (0.009)	0.064 (0.012)
$$\widehat{\mathit{\text{FDR}}}$$	0.021 (0.004)	0.031 (0.005)	0.042 (0.006)
Sensitivity	0.953 (0.011)	0.906 (0.015)	0.862 (0.020)
Specificity	0.995 (0.001)	0.992 (0.002)	0.989 (0.002)

Operating characteristics are based on the Bayes rule. $\mathit{\text{cor}}{({\chi }_g,\widehat{{\chi }_g})}^{\ast }$ is the correlation coefficient between the true difference and the estimated difference.