Probability Filters as a Model of Belief; Comparisons to the Framework of Desirable Gambles

Catrin Campbell-Moore
Proceedings of the Twelveth International Symposium on Imprecise Probability: Theories and Applications, PMLR 147:42-50, 2021.

Abstract

We propose a model of uncertain belief. This models coherent beliefs by a filter, ${F}$, on the set of probabilities. That is, it is given by a collection of sets of probabilities which are closed under supersets and finite intersections. This can naturally capture your probabilistic judgements. When you think that it is more likely to be sunny than rainy, we have$\{ p | p(\textsc{Sunny}\xspace)>p(\textsc{Rainy}\xspace)\} \in {F}$. When you think that a gamble $g$ is desirable, we have $\{ p | \mathrm{Exp}_p[g]>0 \} \in {F}$. It naturally extends the model of credal sets; and we will show it captures all the expressive power of the desirable gambles model. It also captures the expressive power of sets of desirable gamble sets (with a mixing axiom, but no Archimadean axiom).

Cite this Paper

BibTeX
@InProceedings{pmlr-v147-campbell-moore21a, title = {Probability Filters as a Model of Belief; Comparisons to the Framework of Desirable Gambles}, author = {Campbell-Moore, Catrin}, booktitle = {Proceedings of the Twelveth International Symposium on Imprecise Probability: Theories and Applications}, pages = {42--50}, 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/campbell-moore21a/campbell-moore21a.pdf}, url = {https://proceedings.mlr.press/v147/campbell-moore21a.html}, abstract = {We propose a model of uncertain belief. This models coherent beliefs by a filter, ${F}$, on the set of probabilities. That is, it is given by a collection of sets of probabilities which are closed under supersets and finite intersections. This can naturally capture your probabilistic judgements. When you think that it is more likely to be sunny than rainy, we have$\{ p | p(\textsc{Sunny}\xspace)>p(\textsc{Rainy}\xspace)\} \in {F}$. When you think that a gamble $g$ is desirable, we have $\{ p | \mathrm{Exp}_p[g]>0 \} \in {F}$. It naturally extends the model of credal sets; and we will show it captures all the expressive power of the desirable gambles model. It also captures the expressive power of sets of desirable gamble sets (with a mixing axiom, but no Archimadean axiom).} }
Endnote
%0 Conference Paper %T Probability Filters as a Model of Belief; Comparisons to the Framework of Desirable Gambles %A Catrin Campbell-Moore %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-campbell-moore21a %I PMLR %P 42--50 %U https://proceedings.mlr.press/v147/campbell-moore21a.html %V 147 %X We propose a model of uncertain belief. This models coherent beliefs by a filter, ${F}$, on the set of probabilities. That is, it is given by a collection of sets of probabilities which are closed under supersets and finite intersections. This can naturally capture your probabilistic judgements. When you think that it is more likely to be sunny than rainy, we have$\{ p | p(\textsc{Sunny}\xspace)>p(\textsc{Rainy}\xspace)\} \in {F}$. When you think that a gamble $g$ is desirable, we have $\{ p | \mathrm{Exp}_p[g]>0 \} \in {F}$. It naturally extends the model of credal sets; and we will show it captures all the expressive power of the desirable gambles model. It also captures the expressive power of sets of desirable gamble sets (with a mixing axiom, but no Archimadean axiom).
APA
Campbell-Moore, C.. (2021). Probability Filters as a Model of Belief; Comparisons to the Framework of Desirable Gambles. Proceedings of the Twelveth International Symposium on Imprecise Probability: Theories and Applications, in Proceedings of Machine Learning Research 147:42-50 Available from https://proceedings.mlr.press/v147/campbell-moore21a.html.

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