Discussion: Foundations of Statistical
Inference, Revisited
Ryan Martin and Chuanhai Liu
Abstract. This is an invited contribution to the discussion on Profes-
sor 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 theo-
rem lifted, we revisit the foundations of statistical inference, focusing
on some new foundational principles, the inferential model framework,
and connections with sufficiency and conditioning