Statistics Seminar: "Modeling uncertainty with sets of probabilities"

Abstract: Not all uncertainty in statistical modeling can be faithfully captured by a precise probability. One may not know what prior to use for a Bayesian model, what mechanism gave rise to the missing data, or how to make probabilistic statements when non-identifiable parameters are involved. Such kinds of uncertainty are structurally intrinsic to the model, and set of probabilities can well articulate them without concocting unwarranted assumptions.

In this talk, I introduce a novel approach to simultaneous inference using belief function as the modeling vocabulary. Under the ``vacuous orientation’’ assumption, the proposed approach alleviates the need to specify a correlational structure among marginal errors. In contrast to the Bonferroni correction, it produces calibrated posterior inference when testing a large number of collinear hypotheses through recognizing their logical relations. I also discuss challenges with sets of probabilities conditioning, as a choice of rules may give rise to the unsettling posterior phenomena of dilation, contraction and sure loss. These findings underscores the invaluable role of judicious judgment in handling low-resolution probabilistic information.

Host: Todd Kuffner