Rhesus monkey Data [1]
| Dose |
Dead |
Survived |
Total |
| 25 |
1 |
3 |
4 |
| 66 |
2 |
0 |
2 |
| 83 |
2 |
0 |
2 |
| 99 |
1 |
1 |
2 |
| 182 |
3 |
4 |
7 |
| 1111 |
1 |
1 |
2 |
| 1774 |
1 |
1 |
2 |
| 2287 |
1 |
1 |
2 |
| 2586 |
2 |
0 |
2 |
| 3166 |
1 |
1 |
2 |
| 5055 |
6 |
1 |
7 |
| 5519 |
2 |
0 |
2 |
| 5652 |
2 |
0 |
2 |
| 5669 |
1 |
0 |
1 |
| 7459 |
2 |
0 |
2 |
| 9199 |
1 |
1 |
2 |
| 10774 |
2 |
0 |
2 |
| 16790 |
1 |
1 |
2 |
| 41023 |
2 |
0 |
2 |
| 45498 |
1 |
2 |
3 |
| 53206 |
2 |
0 |
2 |
| 55195 |
2 |
0 |
2 |
| 131771 |
1 |
1 |
2 |
| 149175 |
2 |
0 |
2 |
|
Goodness of fit and model selection
| Model |
Deviance |
Δ |
Degrees
of freedom |
χ20.95,1
p-value |
χ20.95,m-k
p-value |
| Exponential |
137 |
113 |
23 |
3.84
0 |
35.2
0 |
| Beta Poisson |
24 |
22 |
33.9
0.345 |
| Beta-Poisson fits better than exponential; cannot reject good fit for beta-Poisson. |
|
Optimized parameters for the beta-Poisson model, from 10000 bootstrap iterations
| Parameter |
MLE estimate |
Percentiles |
| 0.5% |
2.5% |
5% |
95% |
97.5% |
99.5% |
| α |
1.45E-01 |
1.82E-02 |
2.72E-02 |
4.15E-02 |
2.59E-01 |
2.87E-01 |
3.49E-01 |
| N50 |
5.01E+01 |
6.71E-12 |
6.31E-07 |
2.86E-03 |
2.62E+02 |
3.28E+02 |
4.87E+02 |
|
Parameter scatter plot for beta Poisson model ellipses signify the 0.9, 0.95 and 0.99 confidence of the parameters.
beta Poisson model plot, with confidence bounds around optimized model
References
QMRA