Independent Natural Extension for Infinite Spaces: Williams-Coherence to the Rescue

Jasper De Bock
Proceedings of the Tenth International Symposium on Imprecise Probability: Theories and Applications, PMLR 62:121-132, 2017.

Abstract

We define the independent natural extension of two local models for the general case of infinite spaces, using both sets of desirable gambles and conditional lower previsions. In contrast to Miranda and Zaffalon (2015), we adopt Williams-coherence instead of Walley-coherence. We show that our notion of independent natural extension always exists—whereas theirs does not—and that it satisfies various convenient properties, including factorisation and external additivity.

Cite this Paper

BibTeX
@InProceedings{pmlr-v62-de bock17a, title = {Independent Natural Extension for Infinite Spaces: Williams-Coherence to the Rescue}, author = {De Bock, Jasper}, booktitle = {Proceedings of the Tenth International Symposium on Imprecise Probability: Theories and Applications}, pages = {121--132}, year = {2017}, editor = {Antonucci, Alessandro and Corani, Giorgio and Couso, Inés and Destercke, Sébastien}, volume = {62}, series = {Proceedings of Machine Learning Research}, month = {10--14 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v62/de bock17a/de bock17a.pdf}, url = {https://proceedings.mlr.press/v62/de-bock17a.html}, abstract = {We define the independent natural extension of two local models for the general case of infinite spaces, using both sets of desirable gambles and conditional lower previsions. In contrast to Miranda and Zaffalon (2015), we adopt Williams-coherence instead of Walley-coherence. We show that our notion of independent natural extension always exists—whereas theirs does not—and that it satisfies various convenient properties, including factorisation and external additivity.} }
Endnote
%0 Conference Paper %T Independent Natural Extension for Infinite Spaces: Williams-Coherence to the Rescue %A Jasper De Bock %B Proceedings of the Tenth International Symposium on Imprecise Probability: Theories and Applications %C Proceedings of Machine Learning Research %D 2017 %E Alessandro Antonucci %E Giorgio Corani %E Inés Couso %E Sébastien Destercke %F pmlr-v62-de bock17a %I PMLR %P 121--132 %U https://proceedings.mlr.press/v62/de-bock17a.html %V 62 %X We define the independent natural extension of two local models for the general case of infinite spaces, using both sets of desirable gambles and conditional lower previsions. In contrast to Miranda and Zaffalon (2015), we adopt Williams-coherence instead of Walley-coherence. We show that our notion of independent natural extension always exists—whereas theirs does not—and that it satisfies various convenient properties, including factorisation and external additivity.
APA
De Bock, J.. (2017). Independent Natural Extension for Infinite Spaces: Williams-Coherence to the Rescue. Proceedings of the Tenth International Symposium on Imprecise Probability: Theories and Applications, in Proceedings of Machine Learning Research 62:121-132 Available from https://proceedings.mlr.press/v62/de-bock17a.html.

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