Timeline for Is the Gaussian Correlation Inequality universal?
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Apr 11, 2017 at 20:11 | comment | added | Henry.L | Okay, I see your point. thanks for teaching! | |
| Apr 11, 2017 at 20:09 | comment | added | Timothy Chow | @Henry.L : Regarding whether something more general is going on, I do not think that looking at the proof is a reliable indicator, because there are too many cases in mathematics where a result generalizes but the proof does not. Also, people suspected that GCI was true long before the proof existed, so whatever intuitions drove them to conjecture GCI could not have been based on the proof. | |
| Apr 11, 2017 at 18:56 | comment | added | Henry.L | Without any disrespect, I do not see there is anything more general going on since Royden's proof uses Gaussian-ity heavily; nor did I think it is a special property for Gaussian dist only, since we can use central limit theorem to extend the result to a wider range of applications I guess. | |
| Apr 11, 2017 at 18:34 | comment | added | Timothy Chow | The fact that more general distributions satisfy a related but weaker condition is, to me, evidence that something more general is going on, and that GCI is not just a very unusual property that is satisfied only by an extremely special class of probability distributions. | |
| Apr 11, 2017 at 18:32 | comment | added | Timothy Chow | @Henry.L : Well, we certainly cannot expect any results about general convex sets for more general distributions because for general convex sets, even the Gaussian case was intractable until recently! The question is whether we intuitively expect the inequality to generalize to other distributions. In other words, is Royen's use of special properties of Gaussians an artifact of his method of proof? If we think of GCI as a general property of convex sets rather than as an amazing property of a very special distribution then we might expect it to generalize to other distributions. | |
| Apr 11, 2017 at 16:51 | comment | added | Henry.L | GCI is for general convex sets, this is more like a result on bounds of extreme values. But did learn sth, thanks! | |
| Apr 11, 2017 at 16:12 | history | answered | Timothy Chow | CC BY-SA 3.0 |