A Counterexample to Three Imprecise Decision Theories

Imprecise probability trees: Bridging two theories of imprecise probability

We give an overview of two approaches to probability theory where lower and upper probabilities, rather than probabilities, are used: Walley’s behavioural theory of imprecise probabilities, and Shafer and Vovk’s game-theoretic account of probability. We show that the two theories are more closely related than would be suspected at first sight, and we establish a correspondence between them that...

Decision making with imprecise probabilities

In many decision problems the only information available about a random event is expert opinion. The theory of imprecise probabilities, a generalization of standard subjective probability, allows us to deal with such information. In this paper the use of imprecise probabilities is discussed, with emphasis on elicitation and combination of opinions and decision making, and some recent results ar...

Imprecise Probability: Theories and Applications (ISIPTA'13)

Decision Making with Imprecise Probabilities

Orthodox Bayesian decision theory requires an agent’s beliefs representable by a real-valued function, ideally a probability function. Many theorists have argued this is too restrictive; it can be perfectly reasonable to have indeterminate degrees of belief. So doxastic states are ideally representable by a set of probability functions. One consequence of this is that the expected value of a ga...

Novel approach to imprecise assessment and decision environments (NAIADE)