Timeline for Maximum likelihood estimator, exact distribution
Current License: CC BY-SA 3.0
6 events
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| Apr 13, 2017 at 12:44 | history | edited | CommunityBot |
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| Nov 19, 2014 at 23:40 | comment | added | whuber♦ | @Silver I see better what you mean now. That makes sense and it's pretty close to the practice I have personally adopted. One has to be careful because expressions like "$dF$" can also be interpreted as Lebesgue-Stieltjes measures rather than as differential forms (although clearly the two are closely allied). All in all, though, explicitly writing out the differentials can be very helpful in avoiding common mistakes when working with PDFs. It's something I would seriously consider teaching in place of the usual Jacobian formulas. | |
| Nov 19, 2014 at 23:36 | comment | added | Silverfish | The differential forms and their wedge products are all perfectly standard notation, at least among the mathematically inclined - but writing them as part of the PDF isn't standard. It seems to me all the interesting mechanics are happening on the right hand side. So rather than try to redefine the PDF, why not just call the left hand side something else? In particular, why not $dF$? I might not be seeing something, but it seems to me all the useful manipulation on the right side would proceed as before. | |
| Nov 19, 2014 at 23:21 | comment | added | whuber♦ | @Silver Your suggestion would destroy most of the computational advantages. I am using standard notation; it should be recognizable by any first-year math graduate student. It just hasn't filtered down from mathematics into statistics. I don't blame statisticians: despite its suitability to relativity and E&M, it took the better part of the 20th century for physicists to recognize its merits! One way to dodge the issue is to do the calculations however you wish and then announce the results to the world (in your paper or whatever): let the readers check it themselves if they want :-). | |
| Nov 19, 2014 at 23:13 | comment | added | Silverfish | I can see the virtues of forcing the differentials to be more explicit, particularly as an aid for people not used to the idea of a probability density. But it does mean the notation for $f$ no longer matches the standard notation found in textbooks, and would cause raised eyebrows if handed in as part of an assignment! If somebody wanted to keep the mechanics of this approach without abandoning convention, would it suffice to replace e.g. $f$ by $dF$ and $g$ by $dG$ throughout? | |
| Jun 5, 2014 at 14:27 | history | answered | whuber♦ | CC BY-SA 3.0 |