Timeline for Numerical evaluation/approximation of non-central high-order moments of high-dimensional Gaussian measures?
Current License: CC BY-SA 3.0
21 events
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| Apr 7, 2018 at 6:16 | history | edited | Fabrice Pautot | CC BY-SA 3.0 |
Private solution added
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| Mar 4, 2018 at 21:54 | history | edited | Fabrice Pautot | CC BY-SA 3.0 |
added 27 characters in body
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| Feb 6, 2018 at 12:12 | history | edited | Fabrice Pautot | CC BY-SA 3.0 |
added 56 characters in body
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| Feb 3, 2018 at 21:43 | history | edited | Fabrice Pautot | CC BY-SA 3.0 |
typo
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| Feb 3, 2018 at 21:35 | history | edited | Fabrice Pautot | CC BY-SA 3.0 |
typo
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| Feb 2, 2018 at 23:17 | history | edited | Fabrice Pautot | CC BY-SA 3.0 |
maximum corrected
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| Feb 2, 2018 at 23:00 | history | edited | Fabrice Pautot | CC BY-SA 3.0 |
bound on k corrected
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| Feb 2, 2018 at 22:46 | history | edited | Fabrice Pautot | CC BY-SA 3.0 |
Improved, Laplace approximation and ratios added
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| Jan 12, 2018 at 16:04 | comment | added | Fabrice Pautot | @Watson Ladd Monte Carlo is another option but fast and deterministic algorithms such as Laplace's approximation would be much better. I'm surprised not to find decicated, sophisticated algos for this purpose. | |
| Jan 11, 2018 at 23:30 | history | edited | Fabrice Pautot | CC BY-SA 3.0 |
added 6 characters in body
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| Jan 11, 2018 at 22:10 | comment | added | Watson Ladd | What about Monte Carlo? | |
| Jan 11, 2018 at 17:44 | answer | added | Abdelmalek Abdesselam | timeline score: 3 | |
| Jan 11, 2018 at 17:29 | history | edited | Nawaf Bou-Rabee | CC BY-SA 3.0 |
adding a link to wiki entry on Isserlis' Theorem
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| Jan 11, 2018 at 16:03 | comment | added | Fabrice Pautot | @NawafBou-Rabee Another one thphys.uni-heidelberg.de/~amendola/teaching/compstat-hd.pdf, page 28, but you can find plenty of them by yourself. Unfortunately, the Wick-Isserlis formula for moments of order $k$ involve $k!!$ terms. Hence, with $k>>1000$, a different method is required for evaluating my moments. Astonishingly, for the time being, I'm unable to find numerical methods and algorithms for high-order moments of Gaussian r.v.. | |
| Jan 11, 2018 at 14:49 | comment | added | Fabrice Pautot | @NawafBou-Rabee Isserlis on page 11, section 6.1 | |
| Jan 11, 2018 at 14:27 | comment | added | Nawaf Bou-Rabee | Thanks, but where in that reference do they state or give the Wick-Isserlis theorem or formula? | |
| Jan 11, 2018 at 14:20 | comment | added | Fabrice Pautot | @NawafBou-Rabee One nice reference is arxiv.org/pdf/1310.2559.pdf | |
| Jan 11, 2018 at 13:58 | comment | added | lcv | @NawafBou-Rabee The moment generating function of a Gaussian is a Gaussian. Which leads to Isserlis formula. However one can probably obtain a recursive version (integrating by parts). | |
| Jan 11, 2018 at 13:19 | comment | added | Nawaf Bou-Rabee | Have you tried using the moment generating function for a multivariate Gaussian? | |
| Jan 11, 2018 at 12:13 | history | edited | Fabrice Pautot | CC BY-SA 3.0 |
added 12 characters in body; edited title
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| Jan 11, 2018 at 11:15 | history | asked | Fabrice Pautot | CC BY-SA 3.0 |