Probability Filters as a Model of Belief

Proceedings of Machine Learning Research – ISIPTA 2021

We propose representing a (possibly imprecise) epistemic state using a probability filter.

This focuses on judgements on sets of probabilities. When you think that it is more likely to be sunny than rainy, we capture your attitude with a collection of probabilistic judgements including the judgement that p(Sunny)>p(Rainy). Judgement may also be suspended, you might allowing for imprecision.

Coherent such judgements are given when the judgements are closed under finite intersections and supersets. This allows for non-Archimadean behaviour.

The framework is very expressively powerful. It can unify work in the imprecise probability literature on desirable gambles and credal sets.

This paper in particular shows that this captures the desirable gambles model.