On the Distribution of Natural Probability Functions

The purpose of this note is to describe the underlying insights and results obtained by the authors, and others, in a series of papers aimed at modelling the distribution of `natural' probability functions, more precisely the probability functions on f0;1gn which we encounter naturally in the real world as subjects for statistical inference, by identifying such functions with large, random,sentences ofthe propositional calculus. We explain how this approach produces a robust parameterised family of priors, Jn, with several of the properties we might have hoped for in the context, for example marginalisation, invariance under weak renaming, and an emphasis on multivariate probability functions exhibiting high interdependence between features. Keywords. Prior probability, imprecise probability, random rentences, probabilistic reasoning, uncertain reasoning. 1 Motivation The motivation for the research described in this paper can, at least partly, be traced back to our experiences i...

• Type: Conference
• Year: 1999
• Where: ISIPTA
• Authors: Jeff B. Paris, Paul N. Watton, George M. Wilmers
• Keywords: Expert Systems, ISIPTA 1999, Mathematics, Probability Functions, Uncertain Reasoning