Non-bayesian foundations for statistical estimation, prediction, and the ravens example

The paper provides a formal proof that efficient estimates of parameters, which vary as as little as possible when measurements are repeated, may be expected to provide more accurate predictions. The definition of predictive accuracy is motivated by the work of Akaike (1973). Surprisingly, the same explanation provides a novel solution for a well known problem for standard theories of scientific confirmation — the Ravens Paradox. This is significant in light of the fact that standard Bayesian analyses of the paradox fail to account for the predictive utility of universal laws like All ravens are black.I wish to thank Martin Barrett, Ellery Eells, Berent Enç, Branden Fitelson, Dan Hausman, Eric Saidel, Brian Skyrms, Elliott Sober, Mariam Thalos, as well as anonymous reviewer, for helpful suggestions. This research was supported by NSF grant DIR-8822278, and by the Graduate School at the University of Wisconsin, Madison.