Archive for May, 2011

h1

Frequentism and Birnbaum’s Theorem

May 18, 2011

Greg Gandenberger

Frequentists appear to be committed to the sufficiency principle (S) and the conditionality principle (C). However, Birnbaum (1962) proved that (S) and (C) entail the likelihood principle (L), which frequentist methods violate.  To respond adequately to Birnbaum’s theorem, frequentists must place restrictions on (S) and/or (C) that block Birnbaum’s proof and argue that those restrictions are well motivated.  Restricting (C) alone will not suffice, because (S) by itself implies too much of the content of (L) to be compatible with frequentist methods. Specifically, frequentists need to restrict (S) so that it does not apply to mixture experiments some of whose components have respective outcomes with the same likelihood function.  Berger and Wolpert (1988, p. 46) claim that such a restriction would be artificial, but in fact it has a strong frequentist motivation: reduction to the minimal sufficient statistic in such an experiment throws away information about what sampling distribution is appropriate for frequentist inference.  On the other hand, frequentists face difficult challenges in trying to state the restriction they need in a precise and general way.

h1

T-invariance and T-violation

May 13, 2011

Bryan Roberts

The old question of intrinsic properties seems to be intimately connected to the symmetries of time in quantum theory. In particular, there is a precise sense in which, in the absence of internal degrees of freedom, Galilei-invariant quantum mechanics is guaranteed to be time reversal invariant. After illustrating this result, I show how it sheds light on some of the puzzling examples of time reversal violation.