Timeline for Bayesian uninformative priors vs. frequentist null hypotheses: what's the relationship?
Current License: CC BY-SA 3.0
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| May 3, 2013 at 15:01 | comment | added | Dikran Marsupial | To be clear, using the drug example, we don't start by feigning ignorance "Well, maybe this drug has zero effect on people.", we start by assuming the null hypothesis is correct "The drug has zero effect and it is up to the drug company to establish that it does have an effect by showing that the results cannot be adequately explained by random chance". The self-skepticism that this approach provides is why the "null ritual", despite its many faults, is still of practical value in science. | |
| May 3, 2013 at 14:45 | comment | added | Dikran Marsupial | The null itself isn't informative or uninformative, but conventional frequentist hypothesis testing is inherently (and quite rightly) biased towards the H0 (unless you also perform a power analysis). This bias can be compared to a prior, but it would be an informative one. It simply isn't meaningful to compare priors and hypotheses, they serve different purposes in the analysis; note Bayesian also use null hypotheses in hypothesis testing (see my answer to the question) where it serves the same purpose as in frequentist hypothesis testing. | |
| May 3, 2013 at 12:56 | comment | added | Matt Asher | @Dikran Marsupial this is to some extent an endless debate, but from a frequentest perspective I see no way to view the null as "decidedly informative". If this were the case, then failing to reject the null would be viewed as proof of the null (since we "already" have information about the null). IMO all approaches to inference are attempting to answer the same interrelated questions: "How should the data be interpreted?" and "how strong is the case?" | |
| May 3, 2013 at 6:14 | comment | added | Dikran Marsupial | The frequentist null hypothesis does not express maximal ignorance, it starts of assuming that the null hypothesis is true and we should only proceed with the alternative hypothesis if the observations are sufficiently unlikely under H0. It might be argued that null hypothesis testing encodes some prior, but it is a decidedly informative one. In my opinion attempting to interpret frequentist hypothesis testing in Bayesian terms is misguided and a recipe for error; they are not answers to the same question. | |
| May 2, 2013 at 19:07 | vote | accept | jerad | ||
| Mar 17, 2014 at 6:33 | |||||
| May 2, 2013 at 18:13 | history | answered | Matt Asher | CC BY-SA 3.0 |