Precision-imprecision equivalence in a broad class of imprecise hierarchical uncertainty models
type: Item
instance of: scholarly article
title: Precision-imprecision equivalence in a broad class of imprecise hierarchical uncertainty models
zbMATH Open document ID: 1016.60001
DOI: 10.1016/S0378-3758(01)00209-9
published in: Journal of Statistical Planning and Inference
publication date: 2002-08-28T00:00:00Z
review text: The two level hierarchical models are considered. There is a first-order uncertainty model about a phenomenon of an interest. The second-order uncertainty represents the modeler's uncertainty. A subject represents his information using a precise model or an imprecise model. The author shows, that it does not matter, whether we assume, that the underlying ideal first-order model is precise or imprecise (precision-imprecision equivalence). An overview of basic notions of the behavioral theory of imprecise probabilities is given. The author uses the term ``gamble'' and explains the relation to the associated term ``event''. The hierarchical model in terms of lower desirability functions is introduced. The second-order model is studied under assumptions, that the first-order model is precise or imprecise. The behavioral implications of lower desirability functions do not depend on whether the underlying first-order model is assumed to be precise or not. The present model is related to the theory of first-order imprecise probabilities, Bayesian first- and second-order models and the theory of fuzzy probabilities and buying functions.
reviewed by: Pavel Froněk
Mathematics Subject Classification ID: 60A05
Mathematics Subject Classification ID: 62A01
zbMATH DE Number: 1790205
zbMATH Keywords: coherence
zbMATH Keywords: imprecision
zbMATH Keywords: natural extension
author: Gert De Cooman
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1790205