I followed the link of commenter “Epanechnikov” to his blog, where I found, among other things, an uncritical discussion of Richard von Mises’s book, “Probability, Statistics and Truth.”

The bad news is that, based on the evidence of his book, Mises didn’t seem to understand basic ideas of statistical significance. See here, Or at the very least, he was grossly overconfident (which can perhaps be seen from the brash title of his book). This is not the fault of “Epanechnikov,” but I just thought that people should be careful about taking too seriously the statistical philosophy of someone who didn’t think to do a chi-squared test when it was called for. (This is not a Bayesian/non-Bayesian thing; it’s just basic statistics.)

Dear Andrew,

You are right to say that Von Mises' statistical philosophy should not be taken too seriously and your criticism (presented in your article "Going beyond the book") is very fair. To my knowledge, the first objections against the philosophy of von Mises (and especially to his axiom of randomness – the principle of the excluded gambling system ) date back as far as the early 1930s (e.g. Reichenbach, H.: 1932a, 'Axiomatik der Wahrscheinlichkeitsrechnung', Mathematische. Zeitschrift, 34, p594. ). A detailed account of all the objections that had been raised against von Mises' philosophy was given by Fréchet at the Geneva conference of 1937*. That is believed (at least by some**) to be the final nail in von Mises' theory coffin. Despite that, the work of Von Mises has been extremely influential and his intuitions are especially interesting. This was my reason for presenting the basic points of the theory and for encouraging some discussion. I should probably have provided some commentary as it may have appeared that I unquestionably accept it.

Thank you for your notes on this issue

* The proceedings of the conference are available at

http://www.amazon.com/Colloque-Consacre-Theorie-P…

**see for example M. van Lambalgen, Randomness and foundations of probability: von Mises' axiomatisation of random sequences. In T. Ferguson et al (eds.), Probability, Statistics and Game Theory: papers in honour of David Blackwell. Institute for Mathematical Statistics Monograph Series Vol. 20, 1996.