Skip to main content

Table 1 Overview of the prior distributions for the treatment effect β, intercepts αd, and auxiliary parameters γd 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

From: Informed Bayesian survival analysis

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
  1. S denotes a Spike prior distribution, N denotes a Normal prior distribution, and LogN denotes a Log-Normal prior distribution