Timeline for What does it mean to factor a joint distribution?
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
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| Sep 22, 2016 at 14:37 | vote | accept | user1205901 - Слава Україні | ||
| Sep 22, 2016 at 14:34 | comment | added | whuber♦ | @GeoMatt Very nicely done! (+1). Your clear and focused exposition, including appropriate links to terms you use, makes for an admirable answer. | |
| Sep 22, 2016 at 5:58 | history | edited | user1205901 - Слава Україні | CC BY-SA 3.0 |
Added a bit more text from the quoted source
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| Sep 22, 2016 at 5:56 | comment | added | GeoMatt22 | @whuber point taken. Below I actually tried to answer the question that was asked :) | |
| Sep 22, 2016 at 5:53 | answer | added | GeoMatt22 | timeline score: 9 | |
| Sep 22, 2016 at 4:40 | comment | added | whuber♦ | @GeoMatt I'm not quite following what "always holds" means. As the quotation indicates, a factorization of a joint distribution into a marginal and conditional distribution is not unique. Often this can be done in a great many ways. For example, the standard binormal distribution factors into a Uniform$(0,2\pi)$ distribution and a $\chi^2(2)$ distribution (which in this case are independent). | |
| Sep 22, 2016 at 4:33 | comment | added | GeoMatt22 | @whuber yes, I was sloppy. The links I gave explain it better. In areas I run into, the term "factor" would usually not be used for something like Taylor's example, which always holds for any $p(x,y)$. It would normally be associated with conditional independence relationships, I believe? | |
| Sep 22, 2016 at 4:21 | comment | added | whuber♦ | @GeoMatt Usually it's more than that: the factors need meaningful interpretations as marginal and conditional probabilities or probability densities. | |
| Sep 22, 2016 at 4:08 | comment | added | Taylor | If I had to guess it''s saying something about how the joint distribution for two discrete random variables $X$ and $Y$ can be written as $p(x|y)p(y)$ and also $p(y|x)p(x)$. I have no idea what $X$ and $Y$ are, though | |
| Sep 22, 2016 at 4:01 | comment | added | GeoMatt22 | As far as I know, it is literally expressing a probability distribution as a product of factors, i.e. $p=p_1p_2\ldots$. More helpfully, it usually refers to something called graphical models. Wikipedia has some OK examples here and here. (The ones with pictures near the top of the articles. The equations are fine too, but a lot more opaque!) | |
| Sep 22, 2016 at 3:53 | history | asked | user1205901 - Слава Україні | CC BY-SA 3.0 |