Coherent Upper Conditional Previsions Defined by Hausdorff Outer Measures for Unbounded Random Variables

Serena Doria
Proceedings of the Eleventh International Symposium on Imprecise Probabilities: Theories and Applications, PMLR 103:159-166, 2019.

Abstract

A model of upper conditional previsions for bounded and unbounded random variables with finite Choquet integral with respect to the Hausdorff outer and inner measures is proposed in a metric space. They are defined by the Choquet integral with respect to Hausdorff outer measures if the conditioning event has positive and finite Hausdorff outer measure in its dimension, otherwise, when the conditioning event has Hausdorff outer measure equal to zero or infinity in its Hausdorff dimension, they are defined by a 0-1 valued finitely, but not countably, additive probability.

Cite this Paper


BibTeX
@InProceedings{pmlr-v103-doria19a, title = {Coherent Upper Conditional Previsions Defined by Hausdorff Outer Measures for Unbounded Random Variables}, author = {Doria, Serena}, booktitle = {Proceedings of the Eleventh International Symposium on Imprecise Probabilities: Theories and Applications}, pages = {159--166}, year = {2019}, editor = {De Bock, Jasper and de Campos, Cassio P. and de Cooman, Gert and Quaeghebeur, Erik and Wheeler, Gregory}, volume = {103}, series = {Proceedings of Machine Learning Research}, month = {03--06 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v103/doria19a/doria19a.pdf}, url = {http://proceedings.mlr.press/v103/doria19a.html}, abstract = {A model of upper conditional previsions for bounded and unbounded random variables with finite Choquet integral with respect to the Hausdorff outer and inner measures is proposed in a metric space. They are defined by the Choquet integral with respect to Hausdorff outer measures if the conditioning event has positive and finite Hausdorff outer measure in its dimension, otherwise, when the conditioning event has Hausdorff outer measure equal to zero or infinity in its Hausdorff dimension, they are defined by a 0-1 valued finitely, but not countably, additive probability.} }
Endnote
%0 Conference Paper %T Coherent Upper Conditional Previsions Defined by Hausdorff Outer Measures for Unbounded Random Variables %A Serena Doria %B Proceedings of the Eleventh International Symposium on Imprecise Probabilities: Theories and Applications %C Proceedings of Machine Learning Research %D 2019 %E Jasper De Bock %E Cassio P. de Campos %E Gert de Cooman %E Erik Quaeghebeur %E Gregory Wheeler %F pmlr-v103-doria19a %I PMLR %P 159--166 %U http://proceedings.mlr.press/v103/doria19a.html %V 103 %X A model of upper conditional previsions for bounded and unbounded random variables with finite Choquet integral with respect to the Hausdorff outer and inner measures is proposed in a metric space. They are defined by the Choquet integral with respect to Hausdorff outer measures if the conditioning event has positive and finite Hausdorff outer measure in its dimension, otherwise, when the conditioning event has Hausdorff outer measure equal to zero or infinity in its Hausdorff dimension, they are defined by a 0-1 valued finitely, but not countably, additive probability.
APA
Doria, S.. (2019). Coherent Upper Conditional Previsions Defined by Hausdorff Outer Measures for Unbounded Random Variables. Proceedings of the Eleventh International Symposium on Imprecise Probabilities: Theories and Applications, in Proceedings of Machine Learning Research 103:159-166 Available from http://proceedings.mlr.press/v103/doria19a.html.

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