Articles in conference proceedings

1. 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.
   • Abstract
   • paper.pdf
   • arXiv: 2204.07428
   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.
2. 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.
   • Abstract
   • paper.pdf
   • video.mov
   • doi: 978-3-030-58449-8_8
   • arXiv: 2005.03098
   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.
3. 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.
   • Abstract
   • paper.pdf
   • poster.pdf
   • slides.pdf
   • arXiv: 1905.09301
   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.