Keynes and the Society for imprecise probability
When completing my comments on Keynes’ A Treatise On Probability, thanks to an Og’s reader, I found that Keynes is held in high esteem (as a probabilist) by the members of the Society for Imprecise Probability. The goals of the society are set as
The Society for Imprecise Probability: Theories and Applications (SIPTA) was created in February 2002, with the aim of promoting the research on imprecise probability. This is done through a series of activities for bringing together researchers from different groups, creating resources for information, dissemination and documentation, and making other people aware of the potential of imprecise probability models.
The Society has its roots in the Imprecise Probabilities Project conceived in 1996 by Peter Walley and Gert de Cooman and its creation has been encouraged by the success of the ISIPTA conferences.
Imprecise probability is understood in a very wide sense. It is used as a generic term to cover all mathematical models which measure chance or uncertainty without sharp numerical probabilities. It includes both qualitative (comparative probability, partial preference orderings, …) and quantitative modes (interval probabilities, belief functions, upper and lower previsions, …). Imprecise probability models are needed in inference problems where the relevant information is scarce, vague or conflicting, and in decision problems where preferences may also be incomplete.
The society sees J.M. Keynes as a precursor of the Dempster-Schafer perspective on probability, whose Bayesian version is represented in Peter Walley’s book, Statistical Reasoning with Imprecise Probabilities, due to the mention in Keynes’ A Treatise On Probability thanks to the remark made by Keynes (Chapter XV) that “many probabilities can be placed between numerical limits”. Given that the book does not extrapolate on how to take advantage of this generalisation of probabilities, but instead sees it as an impediment to probabilise the parameter space, I would think this remark is more representative of the general confusion made between true (i.e. model related) probabilities and their (observation based) estimates.