Constructing Consonant Predictive Beliefs from Data with Scenario Theory

Marco De Angelis, Roberto Rocchetta, Ander Gray, Scott Ferson
Proceedings of the Twelveth International Symposium on Imprecise Probability: Theories and Applications, PMLR 147:357-360, 2021.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v147-de-angelis21a, title = {Constructing Consonant Predictive Beliefs from Data with Scenario Theory}, author = {De Angelis, Marco and Rocchetta, Roberto and Gray, Ander and Ferson, Scott}, booktitle = {Proceedings of the Twelveth International Symposium on Imprecise Probability: Theories and Applications}, pages = {357--360}, year = {2021}, editor = {Cano, Andrés and De Bock, Jasper and Miranda, Enrique and Moral, Serafı́n}, volume = {147}, series = {Proceedings of Machine Learning Research}, month = {06--09 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v147/de-angelis21a/de-angelis21a.pdf}, url = {https://proceedings.mlr.press/v147/de-angelis21a.html}, 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.} }
Endnote
%0 Conference Paper %T Constructing Consonant Predictive Beliefs from Data with Scenario Theory %A Marco De Angelis %A Roberto Rocchetta %A Ander Gray %A Scott Ferson %B Proceedings of the Twelveth International Symposium on Imprecise Probability: Theories and Applications %C Proceedings of Machine Learning Research %D 2021 %E Andrés Cano %E Jasper De Bock %E Enrique Miranda %E Serafı́n Moral %F pmlr-v147-de-angelis21a %I PMLR %P 357--360 %U https://proceedings.mlr.press/v147/de-angelis21a.html %V 147 %X 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.
APA
De Angelis, M., Rocchetta, R., Gray, A. & Ferson, S.. (2021). Constructing Consonant Predictive Beliefs from Data with Scenario Theory. Proceedings of the Twelveth International Symposium on Imprecise Probability: Theories and Applications, in Proceedings of Machine Learning Research 147:357-360 Available from https://proceedings.mlr.press/v147/de-angelis21a.html.

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