Table 3. Performance of τ under different gamma process priors.
| Scenario | Priora | Mean(Bias)b | ESEc | MSEd | CPe | ||
|---|---|---|---|---|---|---|---|
| η | k0 | c0 | |||||
| I | 0.1 | 1 | 0.01 | 4.97 (0.45) | 0.90 | 0.48 | 95 |
| 1 | 1 | 0.01 | 5.00 (0.04) | 0.90 | 0.49 | 95 | |
| 0.1 | 1 | 0.1 | 4.99 (0.11) | 0.91 | 0.47 | 95 | |
| 1 | 1 | 0.1 | 5.00 (.001) | 0.90 | 0.50 | 95 | |
| 0.1 | 1 | 5 | 4.93 (1.47) | 1.08 | 0.50 | 97 | |
| 1 | 1 | 5 | 5.02 (0.36) | 0.90 | 0.47 | 96 | |
| 0.1 | 1 | 10 | 4.84 (3.16) | 1.13 | 0.59 | 96 | |
| 1 | 1 | 10 | 5.00 (.008) | 0.91 | 0.44 | 96 | |
| *0.9 | 1.33 | 0.1 | 4.99 (0.12) | 0.88 | 0.46 | 96 | |
| *0.9 | 1.33 | 5 | 5.00 (0.09) | 0.79 | 0.52 | 94 | |
| II | 0.1 1 | 0.01 | 4.99 (0.11) | 1.06 | 0.55 | 96 | |
| 1 | 1 | 0.01 | 5.00 (0.04) | 1.05 | 0.54 | 96 | |
| 0.1 | 1 | 0.1 | 1.99 (0.23) | 1.07 | 0.50 | 96 | |
| 1 | 1 | 0.1 | 5.00 (0.09) | 1.05 | 0.52 | 96 | |
| 0.1 | 1 | 5 | 4.89 (2.20) | 1.15 | 0.54 | 97 | |
| 1 | 1 | 5 | 5.02 (0.34) | 0.98 | 0.53 | 96 | |
| 0.1 | 1 | 10 | 4.83 (3.42) | 1.17 | 0.69 | 97 | |
| 1 | 1 | 10 | 5.01 (0.26) | 0.95 | 0.50 | 95 | |
| *1.1 | 0.8 | 0.1 | 4.99 (0.24) | 1.05 | 0.51 | 96 | |
| *1.1 | 0.8 | 5 | 5.01 (0.17) | 1.05 | 0.58 | 97 | |
| III | 0.1 | 1 | 0.01 | 4.99 (0.21) | 0.97 | 0.49 | 96 |
| *1 | 1 | 0.01 | 5.00 (0.08) | 0.97 | 0.54 | 96 | |
| 0.1 | 1 | 0.1 | 5.01 (0.07) | 0.98 | 0.52 | 95 | |
| 1 | 1 | 0.1 | 4.99 (0.23) | 0.98 | 0.51 | 95 | |
| 0.1 | 1 | 5 | 4.92 (1.75) | 1.11 | 0.53 | 97 | |
| *1 | 1 | 5 | 5.01 (0.28) | 0.93 | 0.53 | 95 | |
| 0.1 | 1 | 10 | 4.82 (3.43) | 1.14 | 0.60 | 97 | |
| *1 | 1 | 10 | 5.00 (.007) | 0.92 | 0.50 | 95 | |
scenarios denoted by * are those when the prior matches the true distribution
average of the posterior means over 1000 data sets (bias is defined as |(Mean − 5)/5 × 100|)
average of the posterior standard deviation over 1000 data sets
mean square error
coverage of the 95 percentage HPD interval