Timeline for Inference in binomial with zero successes and fixed number of trials
Current License: CC BY-SA 4.0
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| Jan 10, 2022 at 19:50 | comment | added | BruceET | My note shows that the influence of the prior is not great for sample sizes as large as 50 and (especially) 500. The choice probably depends on one's comfort level with Bayesian or frequentist methods. // I did not intend my Answer to contradict approaches suggested in Comments. For practical purposes results are similar. // The intervals shown in the note are sometimes called Jeffreys confidence intervals and used by frequentists. | |
| Jan 10, 2022 at 19:37 | history | edited | BruceET | CC BY-SA 4.0 |
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| Jan 10, 2022 at 19:30 | comment | added | William M. | The corresponding $\alpha = 0.05$ intervals of the method I mentioned are $(0, 0.058155)$ for $n = 50$ and $(0, 0.00597)$ for $n = 500.$ Very similar intervals (the second one more so), yet I feel to use $(0, 1 - \alpha^{\frac{1}{n}})$ is simpler and the underlying assumptions may be also easier to believe. (There is always the issue of the prior being Beta and so on. And yes, this is not a mathematical point but a philosophical one.) What do you think? | |
| Jan 10, 2022 at 19:13 | history | answered | BruceET | CC BY-SA 4.0 |