Research Article

Power Prior Elicitation in Bayesian Quantile Regression

Table 1

Posterior means, posterior standard deviations (SD), and mean of the true values of 𝛽 ( 𝑝 ) .

𝑝 ( 𝛿 0 , 𝜆 0 ) ( 𝜇 𝑎 0 , 𝜎 𝑎 0 ) Mean 𝛽 ( 𝑝 ) SD 𝛽 ( 𝑝 ) Mean of the true values of 𝛽 ( 𝑝 )

0.90(5,5)(0.50, 0.151) 6.410 0.2348 6.7816
(20,20) (0.50, 0.078) 6.735 0.2514
(30,30) (0.50, 0.064) 6.776 0.2326
(50,1)(0.98, 0.019) 6.837 0.2311
(100,1)(0.99, 0.010)6.843 0.2260

0.75 (5,5) (0.50, 0.151)5.7710.15636.1745
(20,20) (0.50, 0.078)5.9910.1692
(30,30) (0.50, 0.064)6.0250.1668
(50, 1) (0.98, 0.019)6.0940.1635
(100,1) (0.99, 0.010)6.1090.1609

0.50(5,5)(0.50, 0.151)5.0970.15595.5000
(20,20) (0.50, 0.078)5.2730.1477
(30,30) (0.50, 0.064)5.3160.1451
(50,1)(0.98, 0.019)5.3820.1424
(100,1)(0.99, 0.010)5.3830.1411

0.25(5,5)(0.50, 0.151)4.4660.16224.8255
(20,20) (0.50, 0.078)4.6000.1464
(30,30) (0.50, 0.064)4.6140.1607
(50,1)(0.98, 0.019)4.6450.1523
(100,1)(0.99, 0.010)4.6450.1437

0.10(5,5)(0.50, 0.151)3.9110.22504.2185
(20,20) (0.50, 0.078)3.9930.2066
(30,30) (0.50, 0.064)4.0190.2014
(50, 1)(0.98, 0.019)4.0380.1990
(100,1)(0.99, 0.010)4.0530.1965