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Arne Decadt, Alexander Erreygers, Jasper De Bock & Gert de Cooman.
Decision-making with E-admissibility given a finite assessment of choices.
In the proceedings of the
10th International Conference on Soft Methods in Probability and Statistics (SMPS 2022),
Sep. 2022.
Given information about which options a decision-maker definitely rejects from given finite sets of options, we study the implications for decision-making with E-admissibility. This means that from any finite set of options, we reject those options that no probability mass function compatible with the given information gives the highest expected utility. We use the mathematical framework of choice functions to specify choices and rejections, and specify the available information in the form of conditions on such functions. We characterise the most conservative extension of the given information to a choice function that makes choices based on E-admissibility, and provide an algorithm that computes this extension by solving linear feasibility problems.
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Arne Decadt, Jasper De Bock & Gert de Cooman.
Inference with choice Functions made practical.
In the proceedings of the
14th International Conference on Scalable Uncertainty Management (SUM 2020),
Sep. 2020.
We study how to infer new choices from previous choices in a conservative manner. To make such inferences, we use the theory of choice functions: a unifying mathematical framework for conservative decision making that allows one to impose axioms directly on the represented decisions. We here adopt the coherence axioms of De Bock and De Cooman (2019). We show how to naturally extend any given choice assessment to such a coherent choice function, whenever possible, and use this natural extension to make new choices. We present a practical algorithm to compute this natural extension and provide several methods that can be used to improve its scalability.
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Arne Decadt, Gert de Cooman & Jasper De Bock.
Monte Carlo Estimation for Imprecise Probabilities: Basic Properties.
In the proceedings of the
11th International Symposium on Imprecise Probability: Theories and Applications (ISIPTA 2019),
Jun. 2019.
We describe Monte Carlo methods for estimating lower envelopes of expectations of real random variables. We prove that the estimation bias is negative and that its absolute value shrinks with increasing sample size. We discuss fairly practical techniques for proving strong consistency of the estimators and use these to prove the consistency of an example in the literature. We also provide an example where there is no consistency.