Timeline for What does "$\sim$" mean and $A | B \sim C$?
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 11, 2014 at 13:17 | vote | accept | Iancovici | ||
| Feb 10, 2014 at 20:52 | comment | added | Zen | whuber: you find it confusing because each instance of the Dirichlet Process is a distribution. | |
| Feb 10, 2014 at 20:31 | comment | added | whuber♦ | The statement "$\theta_{ij} | G_j \sim G_j$" uses "$G_j$" in the role of parameter-cum-random variable (in its first appearance) and of distribution (in its second appearance). That's very explicit--and extraordinarily confusing. Lexically it looks like a self-reference, but evidently it's not. | |
| Feb 10, 2014 at 19:14 | comment | added | jerad | @whuber, I'm not seeing any explicit reference by the authors to $G_j$ as a parameter, but I would not be terribly surprised if they do, as $G_j$ is in fact a distribution that is random. In a topic model with an HDP prior, $G_j$ is the topic weights for the $j^{th}$ document, as explained on page 18. | |
| Feb 10, 2014 at 19:13 | comment | added | whuber♦ | It's just that I found this (ab)use of notation to be extremely confusing (which makes me sympathetic to the O.P.). Parameters and their distributions are such different mathematical objects that this overloading looks awfully ambiguous. | |
| Feb 10, 2014 at 19:09 | comment | added | Andre Silva | @whuber, for what I understood $G_j$ can be both a distribution and also a parameter inside a DP process (last paragraph, page 8, equations 13 and 14). I would try to resolve the "apparent overloading of meanings" checking in which side of ~ the term $G_j$ is (if left: random measurements, if right: specific distribution. If $G_j$ is inside brackets it would indicate a parameter from the distribution. But I have a feeling this is not what you asked, is it? | |
| Feb 10, 2014 at 18:37 | comment | added | whuber♦ | How do you resolve the apparent overloading of meanings where the authors use (for instance) the term "$G_j$" both in the role of distribution and parameter? | |
| Feb 10, 2014 at 18:34 | history | answered | Andre Silva | CC BY-SA 3.0 |