ML Anthology

The Total Belief Theorem

Chunlai Zhou, Fabio Cuzzolin
UAI 2017
/uai/2017/zhou2017uai-total/

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 functions, 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.

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Cite

Text

Zhou and Cuzzolin. "The Total Belief Theorem." Conference on Uncertainty in Artificial Intelligence, 2017.

Markdown

[Zhou and Cuzzolin. "The Total Belief Theorem." Conference on Uncertainty in Artificial Intelligence, 2017.](https://mlanthology.org/uai/2017/zhou2017uai-total/)

BibTeX

@inproceedings{zhou2017uai-total,
  title     = {{The Total Belief Theorem}},
  author    = {Zhou, Chunlai and Cuzzolin, Fabio},
  booktitle = {Conference on Uncertainty in Artificial Intelligence},
  year      = {2017},
  url       = {https://mlanthology.org/uai/2017/zhou2017uai-total/}
}