A Study of the Set of Probability Measures Compatible with Comparative Judgements

We consider a set of comparative probability judgements over a finite possibility space and study the structure of the set of probability measures that are compatible with them. We relate the existence of some compatible probability measure to Walley’s behavioural theory of imprecise probabilities,...

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Detalles Bibliográficos
Autores principales: Erreygers, Alexander, Miranda, Enrique
Formato: Online Artículo Texto
Lenguaje:English
Publicado: 2020
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7274736/
http://dx.doi.org/10.1007/978-3-030-50143-3_13
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author Erreygers, Alexander
Miranda, Enrique
author_facet Erreygers, Alexander
Miranda, Enrique
author_sort Erreygers, Alexander
collection PubMed
description We consider a set of comparative probability judgements over a finite possibility space and study the structure of the set of probability measures that are compatible with them. We relate the existence of some compatible probability measure to Walley’s behavioural theory of imprecise probabilities, and introduce a graphical representation that allows us to bound, and in some cases determine, the extreme points of the set of compatible measures. In doing this, we generalise some earlier work by Miranda and Destercke on elementary comparisons.
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spelling pubmed-72747362020-06-08 A Study of the Set of Probability Measures Compatible with Comparative Judgements Erreygers, Alexander Miranda, Enrique Information Processing and Management of Uncertainty in Knowledge-Based Systems Article We consider a set of comparative probability judgements over a finite possibility space and study the structure of the set of probability measures that are compatible with them. We relate the existence of some compatible probability measure to Walley’s behavioural theory of imprecise probabilities, and introduce a graphical representation that allows us to bound, and in some cases determine, the extreme points of the set of compatible measures. In doing this, we generalise some earlier work by Miranda and Destercke on elementary comparisons. 2020-05-15 /pmc/articles/PMC7274736/ http://dx.doi.org/10.1007/978-3-030-50143-3_13 Text en © Springer Nature Switzerland AG 2020 This article is made available via the PMC Open Access Subset for unrestricted research re-use and secondary analysis in any form or by any means with acknowledgement of the original source. These permissions are granted for the duration of the World Health Organization (WHO) declaration of COVID-19 as a global pandemic.
spellingShingle Article
Erreygers, Alexander
Miranda, Enrique
A Study of the Set of Probability Measures Compatible with Comparative Judgements
title A Study of the Set of Probability Measures Compatible with Comparative Judgements
title_full A Study of the Set of Probability Measures Compatible with Comparative Judgements
title_fullStr A Study of the Set of Probability Measures Compatible with Comparative Judgements
title_full_unstemmed A Study of the Set of Probability Measures Compatible with Comparative Judgements
title_short A Study of the Set of Probability Measures Compatible with Comparative Judgements
title_sort study of the set of probability measures compatible with comparative judgements
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7274736/
http://dx.doi.org/10.1007/978-3-030-50143-3_13
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