## Keynes and the Society for imprecise probability

**W**hen 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 Projectconceived 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.

**T**he 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*. 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.

**between**numerical limits”
October 19, 2010 at 7:11 am

[...] averages any further. For the same reason, I also abstained from relating the book to the notion of uncertain probabilities, despite a nice suggestion by Michael Brady, as I felt this was not directly related to the [...]

October 23, 2010 at 8:38 pm

I understand that you want to limit the content of your paper to certain specific areas.However,the core of the TP (chapters 15,17,20 and 22) is Keynes’s interval estimate aproach to probability using upper and lower bounds ,instead of precise numerical answers,that Keynes derived from Boole.All of Part III of the TP is based on Keynes’s version of Boole’s Problem X.

Similarly,Keynes’s interest in Chebyshev’s Inequality is actually due to his decision theoretic criterion to minimize risk( Least Risk ) rule from chapter 26 which is the first exposition of a safety first rule in history .Roy’s safety first rule also requires the use of Chebyshev’s Inequality.

July 24, 2010 at 9:58 pm

I believe that you need to go on beyond the quote on p.160 of the TP (1921) and work through the 5 problems on pp.162-163 of the TP.You can then move on to chapter 17 of the TP and work out an additional 12 problems worked out completely by Keynes on pp.186-194 of the TP. The problem on pp.192-194,modified by Keynes from Boole ( I assume that you realize that Keynes’s approach to probability is very similar to Booles’s even though Keynes incorrectly evaluated the Boolean approach)in chapters 20 and 22 .this modified problem is central to Keynes’s views on induction and analogy.

July 2, 2010 at 12:08 am

[...] Following the two past PhD courses on Jeffreys‘ Theory of Probability and Keynes‘ Treatise On Probability, I will propose next year a reading course at CREST on [...]

March 30, 2010 at 3:42 am

Actually, I didn’t know it either. When I was an economics estudent, a professor of mine told me that to fully understand Keynes argument about uncertainty in economics (specially in the book The General Theory…) it was necessary to read his Treatise on Probability.

I kept that in mind and was surprised to see in your blog that most of the book was philosophical and have very little technical matter on probability.

Anyway, it i interesting to read your comments about the book, even if I can’t fully understand them.