On Wednesday, October 17 the all-Russian seminar "Mathematical methods of decision analysis in economics, finance and politics" was hold.

Speaker: Andrey Bronevich (HSE)
Title: "Uncertainty measures in the theory of imprecise probabilities"

Speaker: Andrey Bronevich (HSE)
Title: "Uncertainty measures in the theory of imprecise probabilities"

 

Abstract. The theory of imprecise probabilities is the generalization of the classical probability theory. Thisgeneralizationconsistsinthefollowing. The classical probability theory works with single probability distributions, but the theory of imprecise probabilities works with a family of probability measures in general. This allows us to model adequately various types of uncertainty: imprecision, randomness, and incompleteness of information. In the presentation various models of imprecise probabilities are considered – credal sets, belief functions, 2-monotone measures, and also the axiomatic definition on such models uncertainty measures which are similar to Shannon entropy. In the talk the basic principles of the theory of imprecise probabilities are also discussed – independence, natural extension, products of monotone measures and credal sets. The presentation contains both well-known and recently obtained results in the theory of imprecise probabilities.