4 ms·

This one of many Bayesian vs. frequentist blog posts where the frequentist example is presented in such bad faith or is so wrong that it's impossible to take se

This one of many Bayesian vs. frequentist blog posts where the frequentist example is presented in such bad faith or is so wrong that it's impossible to take seriously. Why is the sample mean used for the frequentist CI when it is not a sufficient statistic, and especially since it appears after the section discussing a "common sense approach" in which the author does mention a sufficient statistic: min(D)? All this blog post shows is reasonable bayesian approaches are better than frequentist approaches where common sense isn't allowed.

fenomas 8y ago
Unless I'm missing something the author answers that here: > 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.
- lucienlecam 8y ago
  In other words, the author has no mathematical examples to support the argument, and the objection is purely philosophical...
  - fenomas 8y ago
    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".
    - lucienlecam 8y ago
      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.

fenomas 8y ago

Unless I'm missing something the author answers that here: > 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.

lucienlecam 8y ago
In other words, the author has no mathematical examples to support the argument, and the objection is purely philosophical...
- fenomas 8y ago
  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".
  - lucienlecam 8y ago
    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.