Talk Title: On Statistical Modelling with Imprecise Probabilities
Abstract: By their generalized understanding of uncertainty, imprecise probability methods promise to be powerful also in statistical modelling. The talk discusses this claim in the context of some prototypic areas of
application. We first recall how imprecise probabilistic models provide a natural superstructure upon robustness aspects in frequentist and Bayesian approaches. We then use imprecise priors to model explicitly prior-data conflict. In the second part of the talk we consider several issues in statistical modelling of imprecise data.
In our talk we also distinguish in an ideal typical way between two basic motives for applying imprecise models, which we call ‘defensive view’ and ‘offensive view’. Most applications so far have emphasized the defensive view, understanding imprecise models merely as a tool to avoid unjustified, overprecise modelling assumptions. We also advocate the offensive view by giving examples where weak information from the application area can be powerfully utilized in the estimation of imprecise models, while traditional statistical models would be forced to ignore such valuable information.
Talk Title: Non-Laplacian uncertainty: practical consequences of an ugly paradigm shift about how we handle not knowing
Abstract: The relaxation of the completeness axiom of subjective utility theory leads to a non-LaplacIan kind of uncertainty commonly known as ignorance. Taking account of how this differs from the uncertainty of probability theory will have broad and important implications in engineering, statistics, and medicine. However, the change can be shallow in the sense that practices need not be radically transformed during the shift.
Talk Title: Belief functions and valid statistical inference
Abstract: Belief functions originated with Dempster’s work in statistics, but they are almost entirely absent in the statistics mainstream. In this talk, I will argue that the properties of non-additive belief and plausibility functions are very much in line with classical statistical reasoning (e.g., p-values, confidence, etc) and, furthermore, that non-additivity — and not the familiar additivity of probability measures — is necessary for valid statistical inference. Of course, not all belief functions would be satisfactory in a given problem, and I will present a general inferential model framework for the construction of valid belief functions for statistical inference.