Abstract
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 $\{0,1\}$ 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 parameterised family of priors, $J_n$, 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 sentences, probabilistic reasoning, uncertain reasoning.
The paper is available in the following formats:
Authors addresses:Department of Mathematics,
E-mail addresses:
| Jeff Paris | jeff@ma.man.ac.uk |
| P.N.Watton | none |
| George Wilmers | george@ma.man.ac.uk |
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