`Plausibilities of plausibilities': an approach through circumstances

TL;DR

This paper reinterprets probability-like parameters and their priors in statistical models through the concept of 'circumstances', which are pieces of knowledge satisfying logical properties, linking inferential reasoning to equivalence classes of such knowledge.

Contribution

It introduces a novel interpretation of probability parameters via circumstances, connecting Bayesian inference to logical properties of knowledge pieces.

Findings

Reinterprets priors as classes of circumstances

Links statistical inference to logical properties of knowledge

Provides a new perspective on probability assignment

Abstract

Probability-like parameters appearing in some statistical models, and their prior distributions, are reinterpreted through the notion of `circumstance', a term which stands for any piece of knowledge that is useful in assigning a probability and that satisfies some additional logical properties. The idea, which can be traced to Laplace and Jaynes, is that the usual inferential reasonings about the probability-like parameters of a statistical model can be conceived as reasonings about equivalence classes of `circumstances' - viz., real or hypothetical pieces of knowledge, like e.g. physical hypotheses, that are useful in assigning a probability and satisfy some additional logical properties - that are uniquely indexed by the probability distributions they lead to.