The total belief theorem

Chunlai Zhou, Fabio Cuzzolin
Proceedings of the 33rd Conference on Uncertainty in Artificial Intelligence, PMLR R15:809-818, 2017.

Abstract

In this paper, motivated by the treatment of conditional constraints in the data association problem, we state and prove the generalisation of the law of total probability to belief func- tions, as finite random sets. Our results apply to the case in which Dempster’s conditioning is employed. We show that the solution to the resulting total belief problem is in general not unique, whereas it is unique when the a-priori belief function is Bayesian. Examples and case studies underpin the theoretical contributions. Finally, our results are compared to previous related work on the generalisation of Jeffrey’s rule by Spies and Smets.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR15-zhou17a, title = {The total belief theorem}, author = {Zhou, Chunlai and Cuzzolin, Fabio}, booktitle = {Proceedings of the 33rd Conference on Uncertainty in Artificial Intelligence}, pages = {809--818}, year = {2017}, editor = {Elidan, Gal and Kersting, Kristian}, volume = {R15}, series = {Proceedings of Machine Learning Research}, month = {11--15 Aug}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r15/main/assets/zhou17a/zhou17a.pdf}, url = {https://proceedings.mlr.press/r15/zhou17a.html}, abstract = {In this paper, motivated by the treatment of conditional constraints in the data association problem, we state and prove the generalisation of the law of total probability to belief func- tions, as finite random sets. Our results apply to the case in which Dempster’s conditioning is employed. We show that the solution to the resulting total belief problem is in general not unique, whereas it is unique when the a-priori belief function is Bayesian. Examples and case studies underpin the theoretical contributions. Finally, our results are compared to previous related work on the generalisation of Jeffrey’s rule by Spies and Smets.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T The total belief theorem %A Chunlai Zhou %A Fabio Cuzzolin %B Proceedings of the 33rd Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2017 %E Gal Elidan %E Kristian Kersting %F pmlr-vR15-zhou17a %I PMLR %P 809--818 %U https://proceedings.mlr.press/r15/zhou17a.html %V R15 %X In this paper, motivated by the treatment of conditional constraints in the data association problem, we state and prove the generalisation of the law of total probability to belief func- tions, as finite random sets. Our results apply to the case in which Dempster’s conditioning is employed. We show that the solution to the resulting total belief problem is in general not unique, whereas it is unique when the a-priori belief function is Bayesian. Examples and case studies underpin the theoretical contributions. Finally, our results are compared to previous related work on the generalisation of Jeffrey’s rule by Spies and Smets. %Z Reissued by PMLR on 04 October 2026.
APA
Zhou, C. & Cuzzolin, F.. (2017). The total belief theorem. Proceedings of the 33rd Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R15:809-818 Available from https://proceedings.mlr.press/r15/zhou17a.html. Reissued by PMLR on 04 October 2026.

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