Timeline for Simple example where Bayesian > Frequentist (Unambiguously)?
Current License: CC BY-SA 4.0
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| Aug 6, 2023 at 5:50 | comment | added | Dikran Marsupial | @GrahamBornholt "Fair enough if you find the posterior probability a satisfying answer." a Bayesian could equally say "If you find a procedure that doesn't actually answer the question satisfying". Sorry, I find the frquentist/Baysian antagonism rather tiresome when taken seriously. I made it clear in my answer that both frameworks are useful, both have advantages and disadvantages to those with an open mind about it. " my uncertainty/probability" I have already pointed out objective Bayesianisn, so you have just shown you are ignoring what I have written. | |
| Aug 5, 2023 at 23:59 | comment | added | Graham Bornholt | Fair enough if you find the posterior probability a satisfying answer. Regarding "cookbook" methods, surely the Bayesian approach is full of cookbook methods: conjugate priors, reference priors , etc ...... However difficult integration is, students must ask themselves do we need this. The 'elephant in the room' is surely that many scientists have no interest in someone's posterior probabilities: they are more interested in modelling the data-generating mechanism itself not how my uncertainty/probability is changed by data (IMHO). | |
| Aug 5, 2023 at 21:53 | comment | added | Dikran Marsupial | The Bayesian approach often does directly answer their question (what is the probabilty that the null hypothesis is false) but it isn't well suited to a "cookbook" approach, so if you are not good at integrals, you won't find it easy to use. At the end of the day it is horses for courses and part of the course is the expertise of the user. As long as they are used skeptically even the null ritual is better than nothing. | |
| Aug 5, 2023 at 21:50 | comment | added | Dikran Marsupial | @GrahamBornholt it is a cartoon, the fact that it has a trace of truth in it is what makes it amusing. As it happens, statisticians (including profs that teach statistics) suffer from some of the same misunderstandings, see researchgate.net/publication/… particularly this bit about the survey by Haller and Kraus. The main reason that practitioners get it wrong is that the underlying framework is very subtle and does not directly answer their question (IMHO). | |
| Aug 5, 2023 at 20:58 | comment | added | Graham Bornholt | Perhaps the participants in your cartoon should have been a practitioner and a statistician. | |
| Aug 5, 2023 at 20:54 | comment | added | Graham Bornholt | The importance of scientific context for hypothesis testing has long been stressed in frequentist statistics (Cox(1958) was a great example). Sadly, most practitioners of statistics are not statisticians and this leads to the misuse of p-values, and the failure to take context into account. Statistical inference is only a part of scientific inference. That nonstatisticians misuse statistical tools does not signify a problem with the tools | |
| Aug 4, 2023 at 7:18 | comment | added | Dikran Marsupial | Having taught Bayesian statistics to frequentist statistics students, I have seen their faces when you start talking about integrals on the blackboard. ;o) | |
| Aug 4, 2023 at 7:16 | comment | added | Dikran Marsupial | @GrahamBornholt If you read my answer you would note that I say it is a matter of "horses for courses" - both frameworks have their uses and problems. As it happens most practitioners of frequentist NHSTs make exactly the error that is in the cartoon - not considering prior knowledge in setting the significance level (as Fisher advocated). I was pointing out that prior knowledge is important whether you are a Bayesian or a frequentist. Bayesian probabilities are not necessarily personal, there is such a thing as objectivist Bayesianisn - see Janes etc. | |
| Aug 4, 2023 at 6:51 | comment | added | Graham Bornholt | Thanks for the caricature of the dumb frequentist. Btw, I love how you think it is difficulty with numerical integration that holds back the Bayesian approach. Perhaps you are overestimating the scientific interest in Bayesians' evaluations of their personal uncertainties. | |
| Aug 3, 2023 at 17:39 | history | edited | Dikran Marsupial | CC BY-SA 4.0 |
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| Aug 3, 2023 at 17:31 | history | answered | Dikran Marsupial | CC BY-SA 4.0 |