I realize Eliezer holds great sway on this blog, but I think people here ought to question a bit more closely some of his most winning arguments in favor of casting out frequents for Bayesianism. I've only read this blog around 4 times, and each time I've found a howler apparently accepted. But putting those aside, I find it curious that the results on psychological biases that is given so much weight on this blog are arrived at and affirmed by means of error statistical methodology. error statistics.com
Frequentism is as abused as "orthodox statistics", and in any event, tends to evoke a conception of people interested in direct inference: assigning a probability (based on observed relative frequencies) to outcomes. Frequentism in statistical inference, instead, refers to the use of error probabilities--based on sampling distributions-- in order to assess and control a method's capability to probe a given discrepancy or inferential flaw of interest. Thus, a more suitable name would be error probability statistics, or just error statistics. One i...
I'm sorry to see such wrongheaded views of frequentism here. Frequentists also assign probabilities to events where the probabilistic introduction is entirely based on limited information rather than a literal randomly generated phenomenon. If Fisher or Neyman was ever actually read by people purporting to understand frequentist/Bayesian issues, they'd have a radically different idea. Readers to this blog should take it upon themselves to check out some of the vast oversimplifications... And I'm sorry but Reichenbach's frequentism has very little to do wit...
If there was a genuine philosophy of science illumination it would be clear that, despite the shortcomings of the logical empiricist setting in which Popper found himself , there is much more of value in a sophisticated Popperian methodological falsificationism than in Bayesianism. If scientists were interested in the most probable hypotheses, they would stay as close to the data as possible. But in fact they want interesting, informative, risky theories and genuine explanations. This goes against the Bayesian probabilist ideal. Moreover, you cannot falsif...
No, the multiple comparisons problem, like optional stopping, and other selection effects that alter error probabilities are a much greater problem in Bayesian statistics because they regard error probabilities and the sampling distributions on which they are based as irrelevant to inference, once the data are in hand. That is a consequence of the likelihood principle (which follows from inference by Bayes theorem). I find it interesting that this blog takes a great interest in human biases, but guess what methodology is relied upon to provide evidence of those biases? Frequentist methods.
Y'all are/were having a better discussion here than we've had on my blog for a while....came across by chance. Corey understands error statistics.
Just a couple of points on this discussion, which I'm sure I walked in at the middle of: (1) One thing it illustrates is the important difference between what one "should" believe in the sense of it being prudential in some way, versus a very different notion: what has or has not been sufficiently well probed to regard as warranted (e.g., as a solution to a problem, broadly conceived). Of course, if the problem happens to be "to promote luckiness", a well-tested solution could turn out to be "don't demand well-testedness, but thin... (read more)