Statistics Seminar: "On Valid Prior-Free Probabilistic Inference"
Ryan Martin, NC State University
Abstract: Using probabilities to describe uncertainty in a statistical inference problem is very reasonable approach. Getting probabilities is easy, but ensuring that they are scientifically meaningful/interpretable is not. Indeed, we all take for granted what it means for a probability to be "small" or "large", but I argue that this is actually a practically important issue that requires serious care. Examples will be presented that highlight a fundamental but subtle issue concerning the interpretation of (default-prior) Bayesian posterior probabilities. In light of these concerns, perhaps we need to look beyond Bayes/probability to describe this kind of uncertainty. Towards this, I will introduce a new approach, called inferential models (IMs), built around the theory of random sets, which provides provably valid prior-free probabilistic inference under very general conditions. The IM construction and its key properties will be discussed, along with some examples and further insights.
Hosts: Jose Figueroa-Lopez and Todd Kuffner