Table 1 Overview of the prior distributions for the treatment effect β, intercepts α_d, and auxiliary parameters γ_d across the competing parametric families for both Bayesian model-averaged testing (upper Table) and estimation (lower Table). “Pr. prob.” denotes the prior model probabilities, “Post. prob.” the posterior model probabilities, “log(marglik)” the log of marginal likelihood, and “Incl. BF” the inclusion Bayes factor for including each model into the model ensemble

Bayesian Model-Averaged Testing

Distribution

Prior β

Prior α

Prior γ

Pr. prob

Post. prob

log(marglik)

Incl. BF

Exponential

S(0)

N(8.70, 2.04)

0.10

0.00

5158.39

0.00

Weibull

S(0)

N(8.80, 2.20)

LogN(− 0.07, 0.22)

0.10

0.00

-5151.96

0.00

LogN

S(0)

N(8.70, 1.95)

LogN(0.62, 0.25)

0.10

0.95

-5138.23

182.44

Log-logistic

S(0)

N(8.54, 2.37)

LogN(0.02, 0.27)

0.10

0.03

-5141.65

0.29

Gamma

S(0)

N(8.88, 2.05)

LogN(− 0.10, 0.39)

0.10

0.00

-5149.33

0.00

Exponential

N(0.3, 0.15)_[0,∞]

N(8.70, 2.04)

0.10

0.00

-5162.05

0.00

Weibull

N(0.3, 0.15)_[0,∞]

N(8.80, 2.20)

LogN(− 0.07, 0.22)

0.10

0.00

-5155.86

0.00

LogN

N(0.3, 0.15)_[0,∞]

N(8.70, 1.95)

LogN(0.62, 0.25)

0.10

0.02

-5142.37

0.14

Log-logistic

N(0.3, 0.15)_[0,∞]

N(8.54, 2.37)

LogN(0.02, 0.27)

0.10

0.00

-5145.66

0.01

Gamma

N(0.3, 0.15)_[0,∞]

N(8.88, 2.05)

LogN(− 0.10, 0.39)

0.10

0.00

-5153.30

0.00

Bayesian Model-Averaged Estimation

Distribution

Prior β

Prior α

Prior γ

Pr. prob

Post. prob

log(marglik)

Incl. BF

Exponential

N(0, 1)

N(8.70, 2.04)

0.20

0.00

-5159.70

0.00

Weibull

N(0, 1)

N(8.80, 2.20)

LogN( 0.07, 0.22)

-0.20

0.00

-5153.36

0.00

LogN

N(0, 1)

N(8.70, 1.95)

LogN(0.62, 0.25)

0.20

0.99

-5137.99

363.90

Log-logistic

N(0, 1)

N(8.54, 2.37)

LogN(0.02, 0.27)

0.20

0.01

-5142.50

0.04

Gamma

N(0, 1)

N(8.88, 2.05)

LogN(-0.10, 0.39)

0.20

0.00

-5150.61

0.00