Normal cones corresponding to credal sets of lower probabilities

Škulj, Damjan (avtor)

Credal sets are one of the most important models for describing probabilistic uncertainty. They usually arise as convex sets of probabilistic models compatible with judgments provided in terms of coherent lower previsions or more specific models such as coherent lower probabilities or probability intervals. In finite spaces, credal sets usually take the form of convex polytopes. Many properties of convex polytopes can be derived from their normal cones, which form polyhedral complexes called normal fans. We analyze the properties of normal cones corresponding to credal sets of coherent lower probabilities. For two important classes of coherent lower probabilities, 2-monotone lower probabilities and probability intervals, we provide a detailed description of the normal fan structure. These structures are related to the structure of the extreme points of the credal sets. To arrive at our main results, we provide some general results on triangulated normal fans of convex polyhedra and their adjacency structure.

• Jezik: Angleški jezik
• Ključne besede: normal cone, credal set, convex polyhedron, extreme point, imprecise probability, coherent lower probability
• Vrsta gradiva: Članek v reviji
• Tipologija: 1.01 - Izvirni znanstveni članek
• Organizacija: FDV - Fakulteta za družbene vede
• Status publikacije: Objavljeno
• Različica publikacije: Objavljena publikacija
• Leto izida: 2022
• Št. strani: Str. 35-54
• Številčenje: Vol. 150
• PID: 20.500.12556/RUL-138898
• UDK: 519.2
• ISSN pri članku: 0888-613X
• DOI: 10.1016/j.ijar.2022.08.006
• COBISS.SI-ID: 119057667
• Datum objave v RUL: 24.08.2022

Gradivo je del revije

• Naslov: International journal of approximate reasoning
• Skrajšan naslov: Int. j. approx. reason.
• Založnik: North-Holland
• ISSN: 0888-613X
• COBISS.SI-ID: 14231301

Licence

• Licenca: CC BY-NC-ND 4.0, Creative Commons Priznanje avtorstva-Nekomercialno-Brez predelav 4.0 Mednarodna
• Povezava: http://creativecommons.org/licenses/by-nc-nd/4.0/deed.sl
• Opis: Najbolj omejujoča licenca Creative Commons. Uporabniki lahko prenesejo in delijo delo v nekomercialne namene in ga ne smejo uporabiti za nobene druge namene.

Sekundarni jezik

• Jezik: Slovenski jezik
• Ključne besede: verjetnosti, matematični modeli

Projekti

• Financer: ARRS - Agencija za raziskovalno dejavnost Republike Slovenije
• Številka projekta: P5-0168
• Naslov: Družboslovna metodologija, statistika in informatika