Quantifying Degrees of E-admissibility in Decicion Making with Imprecise Probabilities

Jansen, Christoph; Georg, Schollmeyer and Thomas, Augustin (1. March 2018): Quantifying Degrees of E-admissibility in Decicion Making with Imprecise Probabilities. Department of Statistics: Technical Reports, No.215

Abstract

This paper is concerned with decision making using imprecise probabilities. In the first part, we introduce a new decision criterion that allows for explicitly modeling how far decisions that are optimal in terms of Walley’s maximality are accepted to deviate from being optimal in the sense of Levi’s E-admissibility. For this criterion, we also provide an efficient and simple algorithm based on linear programming theory. In the second part of the paper, we propose two new measures for quantifying the extent of E-admissibility of an E-admissible act, i.e. the size of the set of measures for which the corresponding act maximizes expected utility. The first measure is the maximal diameter of this set, while the second one relates to the maximal barycentric cube that can be inscribed into it. Also here, for both measures, we give linear programming algorithms capable to deal with them. Finally, we discuss some ideas in the context of ordinal decision theory. The paper concludes with a stylized application examples illustrating all introduced concepts.

• Item Type: Paper
• Keywords: Decision Making under Uncertainty; Imprecise Probabilities; E-admissibility; Maximality; Linear Programming; Ordinal Decision Theory; Stochastic Dominance
• Faculties: Mathematics, Computer Science and Statistics > Statistics > Technical Reports
• Subjects: 500 Science > 510 Mathematics
• Language: English