  This is an invited contribution to the discussion on Professor Deborah Mayo's
paper, "On the Birnbaum argument for the strong likelihood principle," to
appear in Statistical Science. Mayo clearly demonstrates that statistical
methods violating the likelihood principle need not violate either the
sufficiency or conditionality principle, thus refuting Birnbaum's claim. With
the constraints of Birnbaum's theorem lifted, we revisit the foundations of
statistical inference, focusing on some new foundational principles, the
inferential model framework, and connections with sufficiency and conditioning.
[arXiv:1302.7021]
