Timeline for Probability of a Gaussian random vector in a cone
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
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| Mar 25, 2022 at 21:29 | vote | accept | Hao He | ||
| Mar 25, 2022 at 5:44 | comment | added | Hao He | Thank you again for the updated answer. The lower bound in your answer is quite good for my research purpose. | |
| Mar 22, 2022 at 23:58 | comment | added | Iosif Pinelis | @HaoHe : Do you have a further response to this answer and the updates? | |
| Mar 18, 2022 at 15:11 | comment | added | Boby | Ok. Thanks a lot. | |
| Mar 18, 2022 at 14:41 | comment | added | Iosif Pinelis | @Boby : I have seen that question and tried to play with it, unsuccessfuly. You are asking completeness-/characterization-type questions, which can be very hard (if at all possible) to answer. | |
| Mar 18, 2022 at 14:10 | comment | added | Boby | Hi Iosif, you seem to be an expert in how to manipulate gaussian. I was wondering if you can take a look at the question I asked here: mathoverflow.net/questions/418204/…. | |
| Mar 18, 2022 at 14:05 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Mar 17, 2022 at 4:21 | comment | added | Iosif Pinelis | @HaoHe : Also, I have just recalled one of my old results, which implies the just added nice lower bound on the probability in question. | |
| Mar 17, 2022 at 4:19 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Mar 17, 2022 at 3:56 | comment | added | Iosif Pinelis | @HaoHe : I tried to differentiate the integral in (2) with respect to $c$, to get $\varphi(c-u\sqrt y)$ in place of $\Phi(c-u\sqrt y)$, where $\varphi:=\Phi'$, but Mathematica cannot take that simpler integral either. However, you can of course analyze the integral by the Laplace method (en.wikipedia.org/wiki/Laplace%27s_method). You can also use asymptotic expansions in the delta method, used in the above answer. | |
| Mar 16, 2022 at 21:40 | comment | added | Hao He | Thanks a lot for your great answer! As I look the equation 2, I am wondering is it possible to approximate (or lower/upper-bound) the $\Phi$ function such that the integral can have a closed-form? | |
| Mar 16, 2022 at 13:22 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Mar 16, 2022 at 0:58 | history | answered | Iosif Pinelis | CC BY-SA 4.0 |