Timeline for Quantifying the confidence that the most sampled outcome is the most probable outcome
Current License: CC BY-SA 4.0
7 events
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| Mar 8, 2023 at 10:34 | vote | accept | Codename 47 | ||
| Mar 5, 2023 at 16:44 | history | edited | kjetil b halvorsen♦ | CC BY-SA 4.0 |
added 38 characters in body
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| Mar 3, 2023 at 9:51 | comment | added | Henry | @cdalitz I tried to warn of the need for some knowledge in probability theory with my introductory words "Using Bayesian methods". I also tried to explain some of the issues with the simplified example of a biased coin. It would be possible to expand this answer into a full lecture including covering uniformity over a standard $(K-1)$-simplex in multidimensional geometry, as well as conjugate distributions and Monte Carlo methods, but it would have got too long. | |
| Mar 3, 2023 at 9:38 | comment | added | cdalitz | Thanks for explaining the simulation. Actually I had to look up the term "conjugate prior" and learn, what parameter set of the Dirichlet distribution corresponds to the uniform distribution and how the prior parameters propagate to the posterior parameters. This helped me understand your answer, but it nevertheless assumes a lot of knowledge in probability theory, which might be beyond the grasp of the original poster. It might be helpful to elaborate somewhat on the underlying ideas in the answer so that more readers can understand it. | |
| Mar 3, 2023 at 9:08 | comment | added | Henry |
@cdalitz each of the million sims generates a random value for the probabilities of each side from the posterior Dirichlet distribution. For example, the first one is 0.1201143 0.1533349 0.2085550 0.2718155 0.2220087 0.0241715 (note these add up to $1$ as they should), and the largest of these is the 4th value. It does this a million times and counts how often each face is the most probable from this sample, reporting the frequency for each, giving a close approximation to the probabilities each face is the most probable in the posterior Dirichlet distribution.
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| Mar 3, 2023 at 8:53 | comment | added | cdalitz | Can you please elaborate a bit on the theory behind your computation? How do you compute or obtain a formula for $P(p_i>p_j\mbox{ for all }j\neq i \mid obs)$? | |
| Mar 2, 2023 at 18:25 | history | answered | Henry | CC BY-SA 4.0 |