Timeline for At what point should we suspect unfair game?
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26 events
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| Jul 25 at 9:25 | comment | added | user6527 | can't actually happen, in which case your "objective" (in the statistical sense) prior is objectively (in the everyday sense) wrong. | |
| Jul 25 at 9:24 | comment | added | user6527 | Regarding informativeness, I think it is the implied subjectivity that some people worry about, but if you have relevant prior knowledge, there will always be an element of subjectivity, but you will get better inferences from less data if you use that prior knowledge. For me, as long as you are clear about what you are doing and why, then subjectivity is fine. It is also worth pointing out that "objective" here is a term of art and doesn't mean what it means in every day speech. There are cases where an "objective" uninformative prior does not rule out something you know | |
| Jul 25 at 9:19 | comment | added | user6527 | @DoubleKnot I am not worried about informative priors - sometimes they are more objective than uninformative ones in a practical sense. In this case, the test statistic is the number of consecutive times (5) the wheel landed on black, so the p-value is calculated from a test statistic (but I didn't explicitly mention a test statistic). I'm afraid I don't understand the last point - it isn't so much a matter of classification or categorization as decision making - deciding what to do, which could be viewed as classification/categorisation of circumstances, but I don't get the nuance there. | |
| Jul 24 at 1:08 | comment | added | Double Knot | Re your worry about subjective priors does philosophy give you informative priors? I'm also surprised with already 7 upvotes no one pointed out your frequentist p-value =0.5^5=0.03125 isn't from a test statistic but likelihood which will become your own linked joke! Finally as for the matrix of confusions of type 1&2 classification errors philosophically there's a subtle difference between classification which is often faced with imbalanced data and categorization which is deterministic collapse as in forcing of sets... | |
| Jul 23 at 17:46 | comment | added | user6527 | @Ray, yes, often a frequentist procedure (e.g. confidence interval) is numerically equivalent to some Bayesian procedure for some particular prior, but the problem is that can't be used as a justification/insight into the frequentist procedure because of the incompatible definition of a probability. However, I think it is better to stick to one framework or the other and be careful not to mix them as that is a source of many of the misinterpretations. Sometimes it is safe, but sometimes it isn't. | |
| Jul 23 at 17:41 | comment | added | Ray | "Unfortunately the threshold where we decide to denounce the casino is difficult to define and depends on prior probabilities, which frequentists often discourage us from using because they are viewed as subjective." Another way to look at it is that there exists a conjugate prior (or possibly a set of them) that is consistent with the manner the hypothesis test and significance threshold are chosen - the frequentist just doesn't know what it is, whereas the Bayesian makes that assumption explicit. | |
| Jul 23 at 12:09 | history | edited | user6527 | CC BY-SA 4.0 |
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| Jul 23 at 12:03 | history | edited | user6527 | CC BY-SA 4.0 |
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| Jul 23 at 11:12 | history | edited | user6527 | CC BY-SA 4.0 |
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| Jul 23 at 11:11 | history | edited | Nikos M. | CC BY-SA 4.0 |
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| Jul 23 at 9:33 | history | edited | user6527 | CC BY-SA 4.0 |
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| Jul 23 at 9:22 | history | edited | user6527 | CC BY-SA 4.0 |
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| Jul 23 at 9:15 | comment | added | user6527 | @DoubleKnot, yes, I'll find a less ambiguous/easily understood wording. I read the question more as how many times does it need to land on black consecutively before we begin to have doubts about fairness, in which case, just waiting for a sufficiently small p-value would do. However the power analysis takes the other (equally valid) view of how many observations would we need before we have seen them. I have a blog post elsewhere about that, which I may link to. I am hoping to add the Bayesian side as well, time permitting. | |
| Jul 23 at 1:09 | comment | added | Double Knot | Importantly to address OP's sample size threshold question for a biased game as a frequentist, a power analysis is required in addition to the initial bias detection either from your NHST or a simpler confidence interval calculation based on normal approximation assuming at least 30 or 40 samples at hand. And are you coming back to cover the missing fully Bayesian posterior + credible interval + Bayes factor power analysis which are supposed to be more natural and superior to NHST significance level and confidence interval?... | |
| Jul 23 at 0:09 | comment | added | Double Knot | Regarding your joke "The error the frequentist is making here is to use a significance level that is far too low because the probability that the sun has actually gone nova is vanishingly small.", did you make a typo here since H0 here is 'the detector is lying to us' which is equivalent to the extremely likely outcome that Sun is not exploding, so a competent frequentist ought to use an abnormally low significance level (compared to the usual 5% suggested by Fisher for most biology or social sciences related NHST cases) to let H0 not be rejected artificially easily like in the joke... | |
| Jul 22 at 14:00 | history | edited | user6527 | CC BY-SA 4.0 |
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| Jul 22 at 13:59 | history | rollback | user6527 |
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| Jul 22 at 13:59 | history | rollback | user6527 |
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| Jul 22 at 13:01 | history | edited | haxor789 | CC BY-SA 4.0 |
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| Jul 22 at 12:28 | history | edited | user6527 | CC BY-SA 4.0 |
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| Jul 22 at 10:20 | history | edited | user6527 | CC BY-SA 4.0 |
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| Jul 22 at 10:09 | history | answered | user6527 | CC BY-SA 4.0 |