Constructing consonant predictive beliefs from data with scenario theory

de Angelis, Marco and Rocchetta, Roberto and Gray, Ander and Ferson, Scott (2021) Constructing consonant predictive beliefs from data with scenario theory. Proceedings of Machine Learning Research, 147. pp. 357-360. ISSN 2640-3498

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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.

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