Timeline for Why is everything based on likelihoods even though likelihoods are so small?
Current License: CC BY-SA 4.0
14 events
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| Feb 21 at 9:16 | comment | added | Sextus Empiricus | @MaxMeijer how is it decided what the standard definition is? Is there some governing body of statistics that decides on this? Or do you speak about the "standard" layman's definition? If the broad definition is confusing to readers then this may be actually good. It is an opportunity to be triggered to educate themselves about the meaning of likelihood. It is not the same as probability. It is about relative probabilities and the value of the constant of proportionality is irrelevant. If 'something has a likelihood of 1', then it is not like saying 'something has a probability of 1'. | |
| Feb 21 at 9:16 | comment | added | Sextus Empiricus | @MaxMeijer Yes, the edits are neither good sources, That was exactly my point that Wikipedia is a bad source. With the links to the edits I justed wanted to sketch how that Wikipedia article about the likelihood function has become the molested article that is is now because people with only clappers are writing about the entire bell. | |
| Feb 21 at 3:24 | comment | added | Michael Lew | @MaxMeijer I am happy to hear that those many (uncited) textbooks have made you so well informed. Perhaps you could extend your reading here: stats.stackexchange.com/questions/97515/… (Please note that I will not respond to any more of your comments.) | |
| Feb 20 at 23:40 | comment | added | Max Meijer | Also, I think that one source that is definitely less reliable than Wikipedia is Wikipedia edits that have been reverted due to false claims, so it may be better to cite a textbook or other authority that uses the broad definition (I can cite many textbooks that contain the Wiki/Wolfram definition) | |
| Feb 20 at 23:35 | comment | added | Max Meijer | While the broad definition isn't completely unheard of apparently, my claim is that it is not the standard definition. Implicitly taking Fisher's definition as your definition may be confusing to readers that were presuming the standard definition was being used, as essentially all of the other answers and comments seem to have done. (Not to mention the wiki and the Wolfram page and most other StackExchange posts on the topic.) | |
| Feb 20 at 17:03 | comment | added | Sextus Empiricus | The old Wikipedia page contained a phrase "and also any other function proportional to such a function" that got rephrased here and eventually deleted here. | |
| Feb 20 at 16:54 | comment | added | Sextus Empiricus | @MaxMeijer it might not be so great to take on a fight about definitions using Wikipedia and Wolfram as your resources (especially the former can be incomplete and narrow depending on the editor). The definition of the likelihood as being proportional to the probability (density) is widely recognised. It is possibly only in Bayesian analysis that people use a more narrow definition such as the user toenails does in their talk on Wikipedia. The older wiki contained proportionality but got removed. | |
| Feb 20 at 6:24 | comment | added | Michael Lew | @MaxMeijer It's no my definition! It's Fisher's. RA Fisher, the guy who introduced the concept. AWF Edwards gives this as the definition in his monograph called Likelihood: "The likelihood, $L(H|R)$, of the hypothesis $H$ given data $R$, and a specific model, is proportional to $P(R|H)$, the constant of proportionality being arbitrary." That accords with Fisher, with Royall, with Pawitan, and with Birnbaum. It's not my definition. | |
| Feb 20 at 0:20 | comment | added | Max Meijer | I've never seen that used as definition in the many books on statistics I've studied. And it is not mentioned on the Wikipedia page nor on the Wolfram page. If you're using a non-standard definition of a term you should indicate that so that people do not become confused. Or you can say that it is the case under your own definition. | |
| Feb 19 at 23:08 | comment | added | Michael Lew | @MaxMeijer The second sentence on that page is totally confused: "Intuitively, the likelihood function [formula] is the probability of observing data $x$ assuming $ \theta$ is the actual parameter." Fisher was quite explicit in his original definition of likelihood (1922): "The likelihood that any parameter (or set of parameters) should have any assigned value (or set of values) is proportional to the probability that if this were so, the totality of the observations should be observed." There are sources far more reliable than a Wikipedia page. | |
| Feb 19 at 22:10 | comment | added | Max Meijer | The likelihood function is not a probability distribution but each likelihood (i.e. for a specific theta) is the probability of the data being observed if the parameter is theta. Just read the second sentence of the Wiki page: en.m.wikipedia.org/wiki/Likelihood_function . The likelihood function multiplied by a constant may happen to be a likelihood function of a different model but not of the same model and sometimes not at all. | |
| Feb 19 at 21:11 | comment | added | Michael Lew | @MaxMeijer Sorry, but you are mistaken. Likelihoods are not probabilities and they remain likelihoods when multiplied by any constant. | |
| Feb 19 at 9:21 | comment | added | Max Meijer | Usually likelihood refers to the probability of the data given the parameter and so the proportionality factor is really part of the definition. If you multiply the whole thing by a constant it won't be the likelihood anymore even though you can still use it to compute the likelihood ratios. | |
| Feb 18 at 2:57 | history | answered | Michael Lew | CC BY-SA 4.0 |