Skip to main content

Imprecise Probability Models of Rational Belief

Periodic Reporting for period 1 - IPMRB (Imprecise Probability Models of Rational Belief)

Reporting period: 2018-08-01 to 2020-07-31

The basic question being addressed by this project is "how should rational agents structure their beliefs?" A standard answer to this question is that probability theory is the correct mathematical model of rational belief: an agent's rational beliefs should conform to the structure of a probability function. This project puts forward several problems with the standard picture, and proposes that an alternative mathematical theory -- the theory of "Imprecise Probabilities" (IP) -- does a better job. This theory is a powerful generalisation of standard probability theory.

Reasoning under uncertainty is something that all kinds of individual, corporate and government actors have to do, and doing so on the basis of the best theory of rational belief will allow better decisions to be made. Since some of the problems with the standard probabilistic theory arise in contexts involving severe uncertainty,
and since Imprecise Probability Models do better in those circumstances, this project is particularly relevant to those working on decision making under severe uncertainty. For example, the success of climate adaptation decisions depends on fine-grained, long-timescale information about extremes of future weather that we don't yet have reliable ways of providing.

The objectives of the project were to produce several research articles on various aspects of IP that, together, provide a solid foundational theory of rational belief, inference and decision making using Imprecise Probabilities; and to disseminate that theory to relevant researcher communities.
The fellow wrote several papers on rational learning and inference using Imprecise Probabilities. These defended the theory from prominent objections in the literature. The fellow also wrote several papers on rational decision making with Imprecise Probabilities, developing a new and distinctive theory of how to choose when you have limited information.

The project work has been presented to and discussed with practitioners from several other disciplines including statistics, economics and climate science. New research connections have been formed that will enhance and facilitate future work on this topic.
Outputs from the project have pushed the boundaries of Imprecise Probability Theory on topics such as: philosophical foundations, decision making, rational inference and change in belief, and, aggregation and group belief. In each case, the work performed towards these goals fits together as part of a cohesive and coherent whole:
a foundationally secure, detailed and workable theory of rationality that has significant advantages over the standard theory. The fellow has engaged sucessfully with researchers in mathematics and statistics and in climate science as well as with the philosophical community.
Picture of the Fellow