E.S. Pearson (11 Aug, 1895-12 June, 1980)
E.S. Pearson died on this day in 1980. Aside from being co-developer of Neyman-Pearson statistics, Pearson was interested in philosophical aspects of statistical inference. A question he asked is this: Are methods with good error probabilities of use mainly to supply procedures which will not err too frequently in some long run? (performance). Or is it the other way round: that the control of long run error properties are of crucial importance for probing the causes of the data at hand? (probativeness). I say no to the former and yes to the latter. But how exactly does it work? It’s not just the frequentist error statistician who faces this question, but also some contemporary Bayesians who aver that the performance or calibration of their methods supplies an evidential (or inferential or epistemic) justification (e.g., Robert Kass 2011). The latter generally ties the reliability of the method that produces the particular inference C to degrees of belief in C. The inference takes the form of a probabilism, e.g., Pr(C|x), equated, presumably, to the reliability (or coverage probability) of the method. But why? The frequentist inference is C, which is qualified by the reliability of the method, but there’s no posterior assigned C. Again, what’s the rationale? I think existing answers (from both tribes) come up short in non-trivial ways.
I’ve recently become clear (or clearer) on a view I’ve been entertaining for a long time. There’s more than one goal in using probability, but when it comes to statistical inference in science, I say, the goal is not to infer highly probable claims (in the formal sense)* but claims which have been highly probed and have passed severe probes. Even highly plausible claims can be poorly tested (and I require a bit more of a test than informal uses of the word.) The frequency properties of a method are relevant in those contexts where they provide assessments of a method’s capabilities and shortcomings in uncovering ways C may be wrong. Knowledge of the methods capabilities are used, in turn, to ascertain how well or severely C has been probed. C is warranted only to the extent that it survived a severe probe of ways it can be incorrect. There’s poor evidence for C when little has been done to rule out C’s flaws. The most important role of error probabilities is in blocking inferences to claims that have not passed severe tests, but also to falsify (statistically) claims whose denials pass severely. This view is in the spirit of E.S. Pearson, Peirce, and Popper–though none fully worked it out. That’s one of the things I do or try to in my latest work. Each supplied important hints. The following remarks of Pearson, earlier blogged here, contains some of his hints.
*Nor to give a comparative assessment of the probability of claims
From Pearson, E. S. (1947)
“How far then, can one go in giving precision to a philosophy of statistical inference?” (Pearson 1947, 172)