Re:Scientists rise up against statistical significance
by lucienlecam on Thursday March 21, 2019 @09:49AM
(#19452269)
In other words, the author has no mathematical examples to support the argument, and the objection is purely philosophical...
Re:Scientists rise up against statistical significance
by fenomas on Thursday March 21, 2019 @11:09AM
(#19453192)
Not as I understand it. Note that the author's argument there isn't "frequentism is bad because it gives an unreasonable answer here", it's "the fact that frequentism gives a different answer here demonstrates that it really is answering a different question".
Re:Scientists rise up against statistical significance
by lucienlecam on Thursday March 21, 2019 @12:47PM
(#19454430)
But the frequentist answer is only different when the frequentist can't use common sense. If you use min(D) as the frequentist estimator, you would get a very different confidence interval, as it would have the form [min(D) - constant, min(D)]. The CDF of the truncated exponential is F(x) = 1-exp(theta-x), and the CDF of the minimum of three samples is 1-(1-F(x))^3. I get that the frequentist 95% CI is [9.00142, 10], which for all intents and purposes is the same as the credible interval the author computes.
I agree that credible intervals and confidence intervals answer different questions. I don't think that it's obvious that the confidence interval approach is wrong, and the example in the blog post is definitely not evidence towards this.
> Edit, November 2014: ... Had we used, say, the Maximum Likelihood estimator or a sufficient estimator like min(x), our initial misinterpretation of the confidence interval would not have been as obviously wrong, and may even have fooled us into thinking we were right. But this does not change our central argument, which involves the question frequentism asks. Regardless of the estimator, if we try to use frequentism to ask about parameter values given observed data, we are making a mistake.