Timeline for What principle protects the objective nature of the prior and the conclusion in Bayes’s theorem?
Current License: CC BY-SA 4.0
28 events
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| Jul 21 at 8:14 | history | reopened |
Johannes Geoffrey Thomas♦ |
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| Jun 28 at 5:27 | comment | added | user6527 | I can't remember the last time I saw a real attempt subjectivist Bayesian analysis (i.e. a numeric one). Sometimes I see the use of informative priors, but they are not being used to represent personal beliefs of the type you mean, but to represent prior knowledge (e.g. that it is extremely difficult to make a coin that is more than very slightly biased). I see plenty of objectivist Bayes analysis though, that use a reference prior with minimial information. | |
| Jun 28 at 5:24 | comment | added | user6527 | @MarkAndrews As I have already said, you use subjective Bayes when discussion your own personal beliefs, you don't use it when discussing reality. In this case, most people would simply reject the posterior because they don't agree with the biased prior. The point is that Bayes rule makes it explicit if the posterior is dominated by the prior because it has all been stated explicitly, | |
| Jun 28 at 0:39 | comment | added | Mark Andrews | @DikranMarsupial. There is nothing unreasonable about the example you describe. However, this example is one that minimizes moral judgment. If we examine "Xanaduvians tend to load the dice more often than other groups do," then the problem reappears. | |
| Jun 27 at 18:53 | comment | added | user6527 | "The hypothesis and the probability of its truth are formed before any evidence is gathered." it is not clear what this means, however I saw six-sided dice long before I ever saw four sided dice, but I didn't need to observe a single roll of a D4 before I had a good probabilistic model for it (a prior belief). What is unreasonable about that? | |
| Jun 27 at 18:50 | comment | added | user6527 | Sadly the edit is not a huge improvement "So what are the set of principles that protect the objective nature of the prior" subjective and objective Bayes are both useful. Why does the objective nature of the prior need "protecting". In objective Bayes the reasons for the prior are normally obvious (ignorance) or well justified (e.g. MaxEnt and invariance), so if you don't agree with the prior, you are free to give objections and/or to specify a better prior. | |
| Jun 27 at 18:46 | comment | added | user6527 | "But the prior seems to be based on nothing." the fact that you know you don't know something is prior knowledge, uninformative priors are used to encode that knowledge (note it is often a reference prior, rather than the users actual belief). | |
| Jun 27 at 17:30 | history | edited | Mark Andrews | CC BY-SA 4.0 |
Complete revision
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| Jun 26 at 13:54 | comment | added | user6527 | BTW anybody that thinks frequentist statistics does not involve prior belief/information is mistaken. A good example is the XKCD "Bayesian -v- frequentist" cartoon (see stats.stackexchange.com/questions/43339/… ) . The error made by the frequentist was not using prior information when deciding on the appropriate significance level should be, which is ignoring the advice of RA Fisher (it is more likely that they just used 0.95 without any thought at all). | |
| Jun 26 at 11:19 | comment | added | user6527 | I'm not sure I can remember the last time I saw someone make a real attempt at a properly subjectivist Bayesian analysis (i.e. a numeric one) where they were actually talking about their personal beliefs. It is one of those things that is talked about rather more than actually done, sadly without distinguishing subjective and objective approaches. | |
| Jun 26 at 11:13 | comment | added | user6527 | It is a shame that this question has been closed. It is unfortunately rather rhetorical in the way it is worded, but there is a factual answer, namely subjectivist Bayesianism is for describing your personal state of knowledge/beliefs. If you are prejudiced or bigoted, then the the analysis will very clearly demonstrate that is the reason for your posterior. What else would you expect? If you want to (try to) make arguments about objective reality, you would use objective Bayes where the prior does not reflect your prior belief but a "reference" state of knowledge (usually ignorance). | |
| Jun 26 at 11:09 | review | Reopen votes | |||
| Jul 21 at 8:14 | |||||
| Jun 25 at 7:54 | history | closed |
g s Lowri David Gudeman Just Some Old Man AnoE |
Opinion-based | |
| Jun 25 at 7:21 | comment | added | Simon Crase | "But suppose the analyst is looking at this hypothesis: all the residents of Xanadu are racists."What is Cromwell's rule and why is it important for Bayesians? | |
| Jun 25 at 3:09 | answer | added | Simon Crase | timeline score: 2 | |
| Jun 24 at 16:51 | answer | added | Ioannis Paizis | timeline score: 2 | |
| Jun 24 at 16:33 | answer | added | Dcleve | timeline score: 1 | |
| Jun 24 at 11:54 | history | became hot network question | |||
| Jun 24 at 11:00 | answer | added | Hart Lort | timeline score: -5 | |
| Jun 24 at 9:04 | answer | added | Professor Sushing | timeline score: 27 | |
| Jun 23 at 19:20 | comment | added | J Kusin | Two people with similar experiences can have very different priors, if that's what you're asking. If there's bias in their reflections, it will influence their assigning priors. And thus their bias will carry through the calculations. Seems like a feature not a bug, and I don't see what needs saving. Not sure if you're going for something more provocative though. | |
| Jun 23 at 19:19 | review | Close votes | |||
| Jun 25 at 7:56 | |||||
| Jun 23 at 19:15 | comment | added | David Gudeman | What is the purpose of using a loaded word like "bigotry" in a philosophical context like this? | |
| Jun 23 at 19:10 | answer | added | Lowri | timeline score: 16 | |
| Jun 23 at 19:07 | answer | added | TKoL | timeline score: 17 | |
| Jun 23 at 18:59 | comment | added | g s | Does this answer your question? Are the priors of Bayesianism really subjective? | |
| Jun 23 at 18:58 | comment | added | causative♦ | The analyst's personal experiences are not the analyst's prior; the prior is what you have before you look at any experiences, theoretically if you were a complete blank slate. Based on the analyst's experiences, Bayes' theorem says how to rationally update the posterior. The evidence you gave for "all the residents of Xanadu are racists" sounds like pretty weak evidence, so Bayes' theorem wouldn't assign a high probability to the statement. | |
| Jun 23 at 18:39 | history | asked | Mark Andrews | CC BY-SA 4.0 |