Timeline for Gaussian expectation restricted to a convex polytope
Current License: CC BY-SA 4.0
16 events
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| Aug 25, 2023 at 19:46 | comment | added | Iosif Pinelis | @MichaelHardy : Hardly far simpler for $n\ge4$. See Plackett's paper linked in my answer. | |
| Aug 25, 2023 at 19:29 | comment | added | Michael Hardy | @IosifPinelis : oh . . . . Somehow I missed the part about the boundaries going straight through the origin. I think that makes it far simpler. | |
| Aug 24, 2023 at 18:27 | history | edited | Ye He | CC BY-SA 4.0 |
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| Aug 24, 2023 at 18:13 | history | edited | Ye He | CC BY-SA 4.0 |
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| Aug 24, 2023 at 18:02 | comment | added | Iosif Pinelis | @MichaelHardy : An expression in elementary functions exists for $n\le3$ -- see my answer (mathoverflow.net/a/453379/36721). The hyperplanes are through the origin; so, your $c$ must be $0$. | |
| Aug 24, 2023 at 17:23 | comment | added | Michael Hardy | I doubt this has a closed form even in the case of the intersection of two half-planes when $n=2.$ If the two half-planes are orthogonal to each other, then it's reducible to two instances of the one-dimensional case. But even the one-dimensional case my require numerical methods: What is $\operatorname E(Z^2\mid Z>c)$ when $Z\sim\operatorname N(0,1)\text{?} \qquad$ | |
| Aug 24, 2023 at 17:15 | history | edited | Michael Hardy | CC BY-SA 4.0 |
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| Aug 24, 2023 at 15:10 | history | edited | Ye He | CC BY-SA 4.0 |
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| Aug 24, 2023 at 14:57 | history | edited | Ye He | CC BY-SA 4.0 |
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| Aug 24, 2023 at 14:57 | comment | added | Ye He | Thanks for the comment. Yes, I mean intersection of half spaces. | |
| Aug 24, 2023 at 14:26 | answer | added | Iosif Pinelis | timeline score: 4 | |
| Aug 24, 2023 at 7:22 | comment | added | Max Horn | You write "hyperplanes" but then describe half spaces. Since you talk about defining a polytope as their intersection, I assume you meant "half spaces"? Please clarify your question either way :-) | |
| Aug 24, 2023 at 6:46 | history | edited | YCor | CC BY-SA 4.0 |
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| Aug 24, 2023 at 3:46 | history | edited | Ye He |
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| S Aug 24, 2023 at 3:35 | review | First questions | |||
| Aug 24, 2023 at 7:23 | |||||
| S Aug 24, 2023 at 3:35 | history | asked | Ye He | CC BY-SA 4.0 |