Timeline for How do Bayesian Statistics handle the absence of priors?
Current License: CC BY-SA 3.0
15 events
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| Feb 4, 2018 at 20:30 | comment | added | Aksakal | If you apply the same prior it means that you literally had not learned ANYTHING since you applied it first time. You ran once how come didn't your beliefs change at all, so you plug the same prior to different data? That's the main issue with Bayesian approach, it's conceptually inconsistent in most applications. We don't search for the submarines everyday | |
| Feb 4, 2018 at 20:15 | comment | added | Xi'an | @Aksakal: This is a caricature of Bayesian analysis! If a sequence of observations cover the same parameter, the corresponding sequence of posteriors is the right construction. If they apply to different parameters for the same model the same prior can (but does not necessarily need to) apply each time. | |
| Feb 3, 2018 at 16:15 | comment | added | Aksakal | @AlecosPapadopoulos, yes, you're supposed to use new prior every time you run a model. You really can't re-run the model! Literally, every time, and almost no practical situation would call for that. Also, everyone has their own prior, you can't use someone else's. Now, I'm not saying that Bayesian can't be used at all. For instance, that famous case of submarine search is the one when it made a sense to apply BAyesian, and it was done consistently. Nobody does this in most cases though | |
| Feb 3, 2018 at 15:17 | comment | added | Alecos Papadopoulos | @Aksakal But why is invalid to use, on Tuesday, as my new prior, the posterior I obtained on Monday? The way I say it, it is a totally valid sequential procedure. So I do not understand why you write "Bayesians are constantly cheating themselves". | |
| Feb 2, 2018 at 19:57 | comment | added | Aksakal | Suppose, you started on a problem on Monday, and had a prior, say standard normal. So, you plug it into your data, run the analysis, learn something. On Tuesday you can't use that prior anymore, because you learned something already. So, you have to plug a different prior, really. So, in strict Bayesian the priors are single use. You literally can run them through the software only ONCE. The moment you get the results, the prior is expired, unless you didn't learn ANYTHING. So in practical sense Bayesian approach is unusable in its pure form, all Bayesians are constantly cheating themselves | |
| Feb 2, 2018 at 19:34 | comment | added | Alecos Papadopoulos | Thanks, I will. Since you mention it, why it is considered cheating, if the data you use for the prior is not used again subsequently in the analysis? | |
| Feb 2, 2018 at 19:27 | comment | added | Tim | @AlecosPapadopoulos empirical Bayes is choosing your priors based on data (i.e. cheating). You can start with Wikipedia or papers by Efron (easily googlable on Google scholar). | |
| Feb 2, 2018 at 19:25 | history | edited | Tim | CC BY-SA 3.0 |
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| Feb 2, 2018 at 18:58 | comment | added | Alecos Papadopoulos | What I "wanted to hear"? As I understand it, when a person poses a question here, it is reasonably expected that the answer will be about the question. There is nothing particular I "wanted to hear" (no priors here too), I just sought answers to specific questions, and my comment was about not seeing in what way your answer addressed my questions. But in your comment I think there is something really relevant: "Empirical Bayes approach"? Can you mention/point to some literature? | |
| Feb 2, 2018 at 18:30 | comment | added | Tim | @AlecosPapadopoulos sorry for not saying what you wanted to hear, but I believe that this is a part of answer for your question. Regarding Q1, obviously assuming uniform prior is not the same as not assuming prior, since you made an assumption. If you don't want to use priors at all, use maximum likelihood or empirical Bayes approach. | |
| Feb 2, 2018 at 18:15 | history | edited | Alexis | CC BY-SA 3.0 |
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| S Feb 2, 2018 at 18:11 | history | suggested | Vladislavs Dovgalecs | CC BY-SA 3.0 |
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| Feb 2, 2018 at 18:02 | comment | added | Alecos Papadopoulos | Your second paragraph is the "you have priors you just don't realize it" argument that I mentioned in my post and had hoped that It wouldn't appear in an answer. As regards your first paragraph, I do not understand whether it contains the answer to the question "Is absence of priors equivalent to an uninformative prior", or not (I am not talking about the distinction between "uniform" and "uninformative"). Does it? | |
| Feb 2, 2018 at 17:41 | review | Suggested edits | |||
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| Feb 2, 2018 at 17:33 | history | answered | Tim | CC BY-SA 3.0 |