Table 13 Heidelberger and welch test for the Bayesian Bernoulli-Exponential model for the bladder cancer data including three prior scenarios
Parameter | Stationarity Test | P-value | Halfwidth Test | Mean | Halfwidth |
|---|---|---|---|---|---|
Informative Prior Scenario | |||||
\(\alpha _{1}\) | passed | 0.499 | passed | 0.222 | 0.019 |
\(\alpha _{2}\) | passed | 0.195 | passed | 0.402 | 0.010 |
\(\alpha _{3}\) | passed | 0.794 | passed | 0.006 | 0.003 |
\(\alpha _{4}\) | passed | 0.462 | passed | -0.049 | 0.006 |
\(\gamma\) | passed | 0.503 | passed | -0.118 | 0.006 |
\(\psi\) | passed | 0.666 | passed | -0.008 | 0.007 |
\(\vartheta\) | passed | 0.207 | passed | 0.000 | 0.003 |
\(\xi\) | passed | 0.618 | passed | -0.127 | 0.004 |
Non- Informative Prior Scenario | |||||
\(\alpha _{1}\) | passed | 0.104 | passed | -0.339 | 0.054 |
\(\alpha _{2}\) | passed | 0.089 | passed | 0.466 | 0.666 |
\(\alpha _{3}\) | passed | 0.555 | passed | 0.107 | 0.010 |
\(\alpha _{4}\) | passed | 0.077 | passed | 0.189 | 0.020 |
\(\gamma\) | passed | 0.542 | passed | -0.021 | 0.013 |
\(\psi\) | passed | 0.322 | passed | 0.106 | 0.011 |
\(\vartheta\) | passed | 0.718 | passed | 0.095 | 0.008 |
\(\xi\) | passed | 0.509 | passed | -0.182 | 0.009 |
Jeffreys Non-Informative Prior Scenario | |||||
\(\alpha _{1}\) | passed | 0.134 | passed | 0.138 | 0.002 |
\(\alpha _{2}\) | passed | 0.433 | passed | 2.005 | 0.016 |
\(\alpha _{3}\) | passed | 0.083 | passed | 0.160 | 0.001 |
\(\alpha _{4}\) | passed | 0.053 | passed | 0.061 | 0.001 |
\(\gamma\) | passed | 0.613 | passed | -0.012 | 0.008 |
\(\psi\) | passed | 0.168 | passed | 0.416 | 0.011 |
\(\vartheta\) | passed | 0.270 | passed | 0.080 | 0.008 |
\(\xi\) | passed | 0.224 | passed | -0.156 | 0.005 |