Timeline for Order of orthant probabilities in a prolate multinormal distribution
Current License: CC BY-SA 4.0
6 events
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| Jan 24, 2023 at 8:17 | comment | added | Jukka Kohonen | By calling Matlab's "mvncdf" from code similar to my answer here. From the documentation, mvncdf is doing quasi-Monte Carlo integration. Since I was searching for discrepancies greater than $0.003$, my negative findings are hardly conclusive of anything, but I could retry with smaller tolerance. (With $k=7$ we have 128 orthants so it is conceivable that any violations of the inequality in question might be numerically small.) | |
| Jan 23, 2023 at 20:52 | comment | added | Iosif Pinelis | @JukkaKohonen : How did you compute the probabilities for $k=6,7$? | |
| Jan 23, 2023 at 5:57 | comment | added | Jukka Kohonen | Thanks; since you have now already answered the k=3 case with squared dot products, I guess I can as well now change the question to use squared dot products as intended. | |
| Jan 22, 2023 at 22:18 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
added 3589 characters in body
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| Jan 22, 2023 at 16:53 | comment | added | Jukka Kohonen | You are right. Here both dot products are negative and $e_1 \cdot u$ has the smaller absolute value, hence is greater. I apologize; I meant to ask about the absolute values (or squares) of the dot products, which would make more sense here. Would you mind if I just edit the question to reflect what I had in mind? Alternatively, I can make a new question. | |
| Jan 22, 2023 at 16:34 | history | answered | Iosif Pinelis | CC BY-SA 4.0 |