Possibilistic Bayesian inference with an application to instrumental variable regression

SPAAM Seminar Series: 11/06/2026 Title: Possibilistic Bayesian inference with an application to instrumental variable regression Speaker: Gregor Steiner, University of Warwick Abstract: Possibility theory offers an alternative to probability theory for representing epistemic uncertainty about a fixed but unknown quantity. In this talk, I will introduce possibility measures as non-additive outer probability measures and explain how these measures admit a Bayesian posterior update in which the prior is a possibility function and normalisation is carried out by maximisation rather than integration, with both conceptual and computational benefits. I will then turn to instrumental variable regression as a concrete application. Identifying valid instruments is difficult, and the treatment effect is only partially identified if the instruments are invalid. I will present a possibilistic approach that performs inference on the treatment effect conditional on a user-specified set of potential instrument validity violations. The resulting uncertainty intervals enjoy a finite-sample coverage guarantee whenever the violation set contains the truth—even with a single, potentially invalid instrument.