Mice/Salmonella strain 216 and 219 data [1]
| Dose |
Dead |
Survived |
Total |
| 5 |
7 |
8 |
15 |
| 25 |
4 |
11 |
15 |
| 125 |
7 |
8 |
15 |
| 630 |
9 |
6 |
15 |
| 3160 |
8 |
7 |
15 |
| 16000 |
13 |
2 |
15 |
| 8E+04 |
15 |
0 |
15 |
| 4E+05 |
15 |
0 |
15 |
| 2E+06 |
15 |
0 |
15 |
| 1E+07 |
15 |
0 |
15 |
|
Goodness of fit and model selection
| Model |
Deviance |
Δ |
Degrees
of freedom |
χ20.95,1
p-value |
χ20.95,m-k
p-value |
| Exponential |
133 |
113 |
9 |
3.84
0 |
16.9
0 |
| Beta Poisson |
20.5 |
8 |
15.5
0.00846 |
| Neither the exponential nor beta-Poisson fits well; beta-Poisson is less bad. |
|
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 |
2.1E-01 |
1.45E-01 |
1.58E-01 |
1.65E-01 |
2.92E-01 |
3.14E-01 |
3.63E-01 |
| N50 |
4.98E+01 |
8.10E+00 |
1.40E+01 |
1.72E+01 |
1.31E+02 |
1.62E+02 |
2.34E+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