|
20 | 20 | "id":"d2ed8640-ca27-4776-be94-6b1763131e07", |
21 | 21 | "metadata": {}, |
22 | 22 | "source": [ |
| 23 | +"# About: Max Ignorance applied to Bernoulli Trials\n", |
23 | 24 | "Context\n", |
24 | 25 | "* See Nassim Taleb's twitter thread on 19th February about Maximum Ignorance\n", |
25 | | -"* Or seeNassim's other posts about the ~\"Surgeon's Problem\"\n", |
| 26 | +"* Or seehis other posts about the ~\"Surgeon's Problem\"\n", |
26 | 27 | "\n", |
27 | 28 | "Given\n", |
28 | 29 | "* Binomial Distribution\n", |
29 | 30 | "* n_samples\n", |
30 | | -"* n_failures (<= n_samples)\n", |
| 31 | +"* n_failures\n", |
31 | 32 | "\n", |
32 | 33 | "Find\n", |
33 | 34 | "* p_event as a function of the observed quantile" |
34 | 35 | ] |
35 | 36 | }, |
| 37 | + { |
| 38 | +"cell_type":"markdown", |
| 39 | +"id":"9a71f141-edff-4314-a34a-7e815737f3ca", |
| 40 | +"metadata": {}, |
| 41 | +"source": [ |
| 42 | +"### Proposed Extension\n", |
| 43 | +"Derive an expected value instead of matching the median for max ignorance\n", |
| 44 | +"\n", |
| 45 | +"Reasoning:\n", |
| 46 | +"* we are equally likely to observe any given percentile when sampling from a binomial distribution (a collection of bernoulli trials/coin flips)\n", |
| 47 | +"* `bernoulli_p` is non linear wrt the binomial distribution percentile observed" |
| 48 | + ] |
| 49 | + }, |
36 | 50 | { |
37 | 51 | "cell_type":"code", |
38 | 52 | "execution_count":2, |
|