Constructing Consonant Predictive Beliefs from Data with Scenario Theory



De Angelis, Marco ORCID: 0000-0001-8851-023X, Rocchetta, Roberto, Gray, Ander ORCID: 0000-0002-1585-0900 and Ferson, Scott ORCID: 0000-0002-2613-0650
(2021) Constructing Consonant Predictive Beliefs from Data with Scenario Theory. In: International symposium on imprecise probability: theory and applications, 2021-07-06 - 2021-07-09, Granada, Spain.

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Abstract

A method for constructing consonant predictive beliefs for multivariate datasets is presented. We make use of recent results in scenario theory to construct a family of enclosing sets that are associated with a predictive lower probability of new data falling in each given set. We show that the sequence of lower bounds indexed by enclosing set yields a consonant belief function. The presented method does not rely on the construction of a likelihood function, therefore possibility distributions can be obtained without the need for normalization. We present a practical example in two dimensions for the sake of visualization, to demonstrate the practical procedure of obtaining the sequence of nested sets.

Item Type: Conference or Workshop Item (Unspecified)
Uncontrolled Keywords: Predictive beliefs, Consonant random sets, Generalization error, Imprecise probability, Evidence theory
Divisions: Faculty of Science and Engineering > School of Engineering
Depositing User: Symplectic Admin
Date Deposited: 17 Jun 2021 08:30
Last Modified: 10 Jun 2022 07:12
URI: https://livrepository.liverpool.ac.uk/id/eprint/3126612