On the structure of probability functions in the natural world

Paris, J.B., Watton, P.N. and Wilmers, G.M. (2000) On the structure of probability functions in the natural world. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 8(3), pp. 311-329. (doi: 10.1142/S0218488500000228)

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Abstract

The purpose of this paper is to describe the underlying insights and results obtained by the authors, and others, in a series of papers aimed at modeling the distribution of 'natural' probability functions, more precisely the probability functions on {0, 1}n which we encounter naturally in the real world as subjects for statistical inference, by identifying such functions with large, random, sentences of the propositional calculus. We explain how this approach produces a robust parameterized 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.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Watton, Dr Paul
Authors: Paris, J.B., Watton, P.N., and Wilmers, G.M.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems
Publisher:World Scientific Publishing
ISSN:0218-4885
ISSN (Online):1793-6411

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