`Plausibilities of plausibilities': an approach through circumstances
arXiv:quant-ph/0607111
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.
30 pages, 3 figures. V2: clarified some points and corrected some typos. V3: corrected typos and added references
References in corpus (5)
- Consistency of the Shannon entropy in quantum experiments
- Numerical Bayesian state assignment for a three-level quantum system. I. Absolute-frequency data; constant and Gaussian-like priors
- Ambiguities in the derivation of retrodictive probability
- The Laplace-Jaynes approach to induction
- The Bloch-vector space for N-level systems -- the spherical-coordinate point of view