Probability and Statistics

Conor Mayo-Wilson (University of Washington, Seattle)
Robins, Ritov, and Wasserman argue that, when a parameter space is infinite-dimensional, principles and intuitions that guide thinking about simpler statistical models are no longer reliable. For this reason, Wasserman concludes that statistics ought to do away completely with "statistical principles" (i.e., purportedly universal axioms about evidence). If sound, RRW's arguments have significant implications for epistemology, philosophy of science, and philosophy of statistics. RRW's argument suggests that philosophers and statisticians ought to exercise extreme care when appealing to toy examples and intuitions to motivate statistical methodology. I argue that RRW's argument itself relies on statistical principles that are false in finite-dimensional settings.

Calvin Burgess (LMU Munich)
Williamson (2007) argued that if probabilities are regular then certain qualitatively identical events must be assigned different probabilities, which is implausible. His remarks suggest an assumption that chances supervene on qualitative local circumstances and space-time invariant laws. Weintraub (2008) responds that Williamson's events differ in their inclusion relations to each other, or between their times, and this can account for their differences in probability. Haverkamp and Schulz (2011) argued against Weintraub, but inconclusively. However, Weintraub's argument ignores the distinction between qualitative differences and mere matters of time and bare identity. It also ignores the relativity of simultaneity. Furthermore, there are other examples where Weintraub's response simply does not hold. There, the qualitatively identical events are entirely disjoint, as are their times and places.

Konstantin Genin (University of Toronto), Kevin T. Kelly (Carnegie Mellon University)
The distinction between deductive (infallible, monotonic) and inductive (fallible, non-monotonic) inference is fundamental in the philosophy of science. However, virtually all scientific inference is statistical, which falls on the inductive side of the traditional distinction. We propose that deduction should be nearly infallible and monotonic, up to an arbitrarily small, a priori bound on chance of error. A challenge to that revision is that deduction, so conceived, has a structure entirely distinct from ideal, infallible deduction, blocking useful analogies from the logical to the statistical domain. We respond by tracing the logical insights of traditional philosophy of science to the underlying information topology over possible worlds, which corresponds to deductive verifiability. Then we isolate the unique information topology over probabilistic worlds that corresponds to statistical verifiability. That topology provides a structural bridge between statistics and logical insights in the philosophy science.