lucienlecam

Heritability (i.e. narrow-sense heritability as typically used in most research articles) is not so clear-cut as to be split between nature and nurture. Even the GP is slightly incorrect when saying:

> ...as opposed to environmental factors

because for heritability, the distinction is between the variance explained by additive genetic effects versus the total variance of the trait of interest. There are other sources of phenotypic variance like epigenetics, non-additive genetic effects, or complex interactions that fall outside the scope of heritability.

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.

In other words, the author has no mathematical examples to support the argument, and the objection is purely philosophical...

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.