Time-slice Bayesianism as a potential solution to the problem of dilation and reflection for imprecise probabilities

Marc Fischer
Proceedings of the Fourteenth International Symposium on Imprecise Probabilities: Theories and Applications, PMLR 290:148-157, 2025.

Abstract

One of the main objections against an imprecise probabilistic framework is the apparent absurdity of dilation when seemingly irrelevant evidence makes your belief in a proposition much less certain than it intuitively ought to be. In this work, after critically analysing an argument by White and refined by Topey, as well as responses by imprecise probabilists, I argue that one way to greatly alleviate the tension this type of case poses is to adopt a form of ’time-slice’ Bayesianism. In the form I envision it, it means that our degrees of belief in A at time $t_i$ are no longer ontologically defined as the result of updating our degrees of belief at time $t_{i-1}$ with the evidence $E_{i-1,i}$ we obtained in between, but as a function of our total evidence available at time $t_i$ and a fundamental prior set of credences. I explain why this move, which forces us to regard all probabilities as conditional probabilities outside time, greatly diminishes the intuitive appeal of dilation-based counterexamples to the soundness of imprecise Bayesianism.

Cite this Paper

BibTeX
@InProceedings{pmlr-v290-fischer25a, title = {Time-slice Bayesianism as a potential solution to the problem of dilation and reflection for imprecise probabilities}, author = {Fischer, Marc}, booktitle = {Proceedings of the Fourteenth International Symposium on Imprecise Probabilities: Theories and Applications}, pages = {148--157}, year = {2025}, editor = {Destercke, Sébastien and Erreygers, Alexander and Nendel, Max and Riedel, Frank and Troffaes, Matthias C. M.}, volume = {290}, series = {Proceedings of Machine Learning Research}, month = {15--18 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v290/main/assets/fischer25a/fischer25a.pdf}, url = {https://proceedings.mlr.press/v290/fischer25a.html}, abstract = {One of the main objections against an imprecise probabilistic framework is the apparent absurdity of dilation when seemingly irrelevant evidence makes your belief in a proposition much less certain than it intuitively ought to be. In this work, after critically analysing an argument by White and refined by Topey, as well as responses by imprecise probabilists, I argue that one way to greatly alleviate the tension this type of case poses is to adopt a form of ’time-slice’ Bayesianism. In the form I envision it, it means that our degrees of belief in A at time $t_i$ are no longer ontologically defined as the result of updating our degrees of belief at time $t_{i-1}$ with the evidence $E_{i-1,i}$ we obtained in between, but as a function of our total evidence available at time $t_i$ and a fundamental prior set of credences. I explain why this move, which forces us to regard all probabilities as conditional probabilities outside time, greatly diminishes the intuitive appeal of dilation-based counterexamples to the soundness of imprecise Bayesianism.} }
Endnote
%0 Conference Paper %T Time-slice Bayesianism as a potential solution to the problem of dilation and reflection for imprecise probabilities %A Marc Fischer %B Proceedings of the Fourteenth International Symposium on Imprecise Probabilities: Theories and Applications %C Proceedings of Machine Learning Research %D 2025 %E Sébastien Destercke %E Alexander Erreygers %E Max Nendel %E Frank Riedel %E Matthias C. M. Troffaes %F pmlr-v290-fischer25a %I PMLR %P 148--157 %U https://proceedings.mlr.press/v290/fischer25a.html %V 290 %X One of the main objections against an imprecise probabilistic framework is the apparent absurdity of dilation when seemingly irrelevant evidence makes your belief in a proposition much less certain than it intuitively ought to be. In this work, after critically analysing an argument by White and refined by Topey, as well as responses by imprecise probabilists, I argue that one way to greatly alleviate the tension this type of case poses is to adopt a form of ’time-slice’ Bayesianism. In the form I envision it, it means that our degrees of belief in A at time $t_i$ are no longer ontologically defined as the result of updating our degrees of belief at time $t_{i-1}$ with the evidence $E_{i-1,i}$ we obtained in between, but as a function of our total evidence available at time $t_i$ and a fundamental prior set of credences. I explain why this move, which forces us to regard all probabilities as conditional probabilities outside time, greatly diminishes the intuitive appeal of dilation-based counterexamples to the soundness of imprecise Bayesianism.
APA
Fischer, M.. (2025). Time-slice Bayesianism as a potential solution to the problem of dilation and reflection for imprecise probabilities. Proceedings of the Fourteenth International Symposium on Imprecise Probabilities: Theories and Applications, in Proceedings of Machine Learning Research 290:148-157 Available from https://proceedings.mlr.press/v290/fischer25a.html.

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