Table 14 Results of the Bayesian Bernoulli-Exponential model applied to the bladder cancer data with different prior scenarios considered
Gaussian Informative Prior Estimates | Deviance Information of Model | |||||||
Parameter | Mean | SD | 2.50% | 97.50% | Dbar | Dhat | DIC | pD |
\(\alpha _{1}\) | 0.621 | 0.263 | 0.113 | 1.136 | 1119 | 1113 | 1126 | 6.652 |
\(\alpha _{2}\) | 0.404 | 0.496 | -0.566 | 1.374 | ||||
\(\alpha _{3}\) | -0.021 | 0.061 | -0.140 | 0.100 | ||||
\(\alpha _{4}\) | -0.115 | 0.095 | -0.300 | 0.068 | ||||
\(\gamma\) | 0.165 | 0.126 | -0.078 | 0.415 | ||||
\(\psi\) | -0.318 | 0.231 | -1.229 | -0.132 | ||||
\(\vartheta\) | 0.070 | 0.090 | -0.109 | 0.248 | ||||
\(\xi\) | -0.366 | 0.094 | -0.550 | -0.187 | ||||
Gaussian Non-Informative Prior Estimates | Deviance Information of Model | |||||||
Parameter | Mean | SD | 0.025 | 0.975 | Dbar | Dhat | DIC | pD |
\(\alpha _{1}\) | 0.256 | 0.312 | -0.321 | 0.867 | 1114 | 1107 | 1121 | 6.953 |
\(\alpha _{2}\) | 0.228 | 0.127 | 0.235 | 0.412 | ||||
\(\alpha _{3}\) | 0.008 | 0.065 | -0.118 | 0.135 | ||||
\(\alpha _{4}\) | -0.006 | 0.107 | -0.206 | 0.198 | ||||
\(\gamma\) | -0.100 | 0.128 | -0.352 | 0.150 | ||||
\(\psi\) | - 0.608 | 0.240 | -1.079 | -0.137 | ||||
\(\vartheta\) | -0.099 | 0.094 | -0.287 | 0.081 | ||||
\(\xi\) | -0.216 | 0.095 | -0.407 | -0.036 | ||||
Jeffreys Non-Informative Prior Estimates | Deviance Information of Model | |||||||
Parameter | Mean | SD | 0.025 | 0.975 | Dbar | Dhat | DIC | pD |
\(\alpha _{1}\) | 0.174 | 0.123 | 0.007 | 0.457 | 1103 | 1098 | 1108 | 4.972 |
\(\alpha _{2}\) | 0.216 | 0.125 | 0.232 | 0.411 | ||||
\(\alpha _{3}\) | 0.036 | 0.029 | 0.001 | 0.108 | ||||
\(\alpha _{4}\) | 0.048 | 0.039 | 0.001 | 0.145 | ||||
\(\gamma\) | 0.055 | 0.129 | -0.199 | 0.305 | ||||
\(\psi\) | -0.408 | 0.241 | -1.009 | -0.135 | ||||
\(\vartheta\) | 0.157 | 0.091 | 0.018 | 0.337 | ||||
\(\xi\) | -0.287 | 0.096 | -0.476 | -0.101 | ||||