Timeline for Using p-value to compute the probability of hypothesis being true; what else is needed?
Current License: CC BY-SA 3.0
12 events
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| Apr 26, 2017 at 21:01 | comment | added | amoeba | Ah, so you are making a distinction between expressions "degree of belief in A" and "probability that A is true"? And further claim that Bayesians (as well as frequentists) should not be using an expression "probability that A is true"? I see. Personally, I'd say that "probability that A is true" is fully synonymous with "probability of A", and according to Bayesian world view (en.wikipedia.org/wiki/Probability_interpretations#Subjectivism), "probability of A" is defined as "degree of belief in A". So it's all the same. | |
| Apr 26, 2017 at 20:47 | comment | added | AdamO | @amoeba well first off, in traditional testing we never actually state an alternative hypothesis. Bayes factors are nice since they require you to say what alternate hypothesis you're after a priori. Bayesian probability is what I take contention with. OP speaks of a hypothesis being true. Bayesian probability is just a degree of belief. However, I don't think belief implies truth. If we had a Bernoulli prior for 0.95 on H_0 vs 0.05 on H_a, I would interpret the 0.95 as a degree of belief for H_0 but not a probability that H_0 is true. To know something as truth requires determination. | |
| Apr 26, 2017 at 20:28 | comment | added | amoeba | I must be missing something, but it seems to me that you are answering a different question than the one asked. OP asked "how to compute the probability that the hypothesis is true?" You are responding to the question "how to determine whether the null hypothesis is true", and argue that this is impossible because statistics does not allow to conclude anything with absolute certainty. Fine; but that's not what OP asked, is it? They asked about computing probability! Or am I missing something here? | |
| Apr 26, 2017 at 16:58 | history | edited | AdamO | CC BY-SA 3.0 | added 1090 characters in body |
| Apr 25, 2017 at 16:01 | comment | added | Dikran Marsupial | @AdamO no, it is possible to use Bayesian statistics without using overconfident priors, it isn't a problem with Bayesian statistics in general, and from what I have read, I don't think Lindley meant it as such. Ironically, the main problem with frequentist statistics is peoples natural desire to interpret them in Bayesian terms - being careful about the meanings of terms and the assumptions is indeed the key. BTW I am an engineer, and am happy with both sets of statistical tools. | |
| Apr 25, 2017 at 15:50 | comment | added | AdamO | @watarok my Scottish Bayesian statistics teacher used that quote regularly, yet never described its relevance. I'm grateful to know it now. | |
| Apr 25, 2017 at 15:46 | comment | added | AdamO | @DikranMarsupial I think the issue of overly confident priors is one that can be applied to all of Bayesian statistics. A non-informative prior often leads to approximate frequentist inference and analysis anyway. The difference is in interpretation: Bayesian results must bandy with the idea of a "truth" or "true parameter". That is fine so long as we carefully describe assumptions, and how power and error rates are fixed. | |
| Apr 25, 2017 at 6:30 | comment | added | Dikran Marsupial | @watarok thanks for the link/clarification, it seems that the mention in the answer is a bit misleading as Lindley is not actually criticizing Bayesian studies, just overly confident priors. | |
| Apr 24, 2017 at 21:20 | comment | added | nwn | @DikranMarsupial Your argument against such use of 0/1 is precisely what the quote is suggesting. It ridicules the situation to explain the necessity of what Lindley calls Cromwell's rule. | |
| Apr 24, 2017 at 16:00 | comment | added | Dikran Marsupial | ""With prior probability 0 that the moon is made of cheese" but given "cogito ergo sum" (and maybe not even that) is all we know for sure, should we give a prior probability of 0 that the moon is made of cheese? 0 and 1 should be reserved for the logically impossible and certain, and eps and 1-eps for statements about the real world. The Bayesian framework is fine, provided your priors accurately represent your prior knowledge of the problem (but that in itself is a problem). | |
| Apr 24, 2017 at 15:08 | history | edited | AdamO | CC BY-SA 3.0 | deleted 4 characters in body |
| Apr 24, 2017 at 15:01 | history | answered | AdamO | CC BY-SA 3.0 |