Timeline for Bound the probability that a point belongs to a set
Current License: CC BY-SA 4.0
16 events
| when toggle format | what | by | license | comment | |
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| Jun 20, 2023 at 9:09 | vote | accept | Star | ||
| Jun 6, 2023 at 17:04 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| S May 8, 2023 at 21:02 | history | bounty ended | CommunityBot | ||
| S May 8, 2023 at 21:02 | history | notice removed | CommunityBot | ||
| May 7, 2023 at 16:02 | answer | added | Iosif Pinelis | timeline score: 2 | |
| May 5, 2023 at 19:59 | comment | added | Star | @IosifPinelis thanks. the proof shows that (2) is a sufficient condition for (1). that's why the final statement involves conditional probabilities ... | |
| May 5, 2023 at 14:52 | comment | added | Iosif Pinelis | I will make one more attempt to try to help you here. The conclusion of your proof involves conditional probabilities, whereas (1) does not. So, your proof may be a proof of something, but it is not a proof of (1). I have not checked steps of your proof. However, I'll reiterate just one more time: "(1) does not need to be proved. What needs to be addressed is my comments on $\nu_{\ell}(b, \theta) $ and $\nu_u(b,\theta)$". | |
| May 5, 2023 at 6:23 | comment | added | Star | I'm sorry but I do not understand the English of "the added proof is not a proof of (1)": do you mean that its steps are wrong? | |
| May 4, 2023 at 18:09 | comment | added | Iosif Pinelis | As I wrote, the added proof is not a proof of (1). Also, (1) does not need to be proved. What needs to be addressed is my comments on $v_\ell(b,\theta)$ and $v_u(b,\theta)$. Otherwise, you cannot possibly get a reasonable answer to your question: as I also said, "The only upper bound under these very general conditions is the trivial bound $1$." | |
| May 4, 2023 at 13:58 | history | edited | Star | CC BY-SA 4.0 |
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| May 4, 2023 at 13:28 | comment | added | Iosif Pinelis | You said you were assuming (1). So, why do you need to prove it? Also, the added proof is, not of (1), but of something else (if it is a proof of anything). You should try, first of all, to address the specific concerns raised in my previous comment. | |
| May 4, 2023 at 11:44 | history | edited | Star | CC BY-SA 4.0 |
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| May 1, 2023 at 13:52 | comment | added | Iosif Pinelis | The only upper bound under these very general conditions is the trivial bound $1$, which is attained when e.g. $v_\ell(b,\theta)=0$ and $v_u(b,\theta)=1$ for all $b,\theta$. You need to specify $v_\ell(b,\theta)$ and $v_u(b,\theta)$ and, I think, the $a_k$'s. However, I am afraid that even then the only upper bound will usually be the trivial bound $1$. You will probably have to rethink the whole thing. | |
| S Apr 30, 2023 at 19:30 | history | bounty started | Star | ||
| S Apr 30, 2023 at 19:30 | history | notice added | Star | Canonical answer required | |
| Apr 27, 2023 at 18:15 | history | asked | Star | CC BY-SA 4.0 |