Posterior Mean

Avg. Percent Error

Pr ${\widehat{\theta }}_{0.1}\in \left[F^{-1}\left(0.1\right)\pm \sigma /\sqrt{n}\right]$

Design

$n=11$

$n=21$

$n=151$

$n=11$

$n=21$

$n=151$

$N\left(\mathrm{0,1}\right)$

−0.0288

−0.0106

−0.0009

0.4995

0.4867

0.4586

$U\left(\mathrm{0,1}\right)$

−0.0921

0.1260

0.0267

0.6919

0.7611

0.6967

$Exp\left(0.5\right)$

−0.6011

0.0588

0.0349

0.9903

0.9882

0.9948

$t\left(\mathrm{0,1,5}\right)$

−0.0970

−0.0460

−0.0058

0.4674

0.4573

0.4349

$0.7\mathcal{N}\left(-\mathrm{1,1}\right)+0.3\mathcal{N}\left({\mathrm{1.5,0.75}}^2\right)$

−0.0137

−0.0040

−0.0006

0.6278

0.6141

0.5848

Posterior Mode

Avg. Percent Error

Pr ${\widehat{\theta }}_{0.1}\in \left[F^{-1}\left(0.1\right)\pm \sigma /\sqrt{n}\right]$

Design

$n=11$

$n=21$

$n=151$

$n=11$

$n=21$

$n=151$

$N\left(\mathrm{0,1}\right)$

0.1714

0.0940

0.0138

0.4313

0.4360

0.4396

$U\left(\mathrm{0,1}\right)$

0.6635

0.3626

0.0524

0.6303

0.6472

0.6623

$Exp\left(0.5\right)$

0.8081

0.4234

0.0585

0.9251

0.9564

0.9900

$t\left(\mathrm{0,1,5}\right)$

0.1626

0.0882

0.0128

0.4173

0.4179

0.4183

$0.7\mathcal{N}\left(-\mathrm{1,1}\right)+0.3\mathcal{N}\left({\mathrm{1.5,0.75}}^2\right)$

0.1269

0.0696

0.0098

0.5496

0.5582

0.5623