Exploring Biased Probability Using Loaded Dice: An Active Learning Exercise with Analogy to Entropic and Energetic Determinants of Equilibria in Chemical Systems
- PhysicsJournal of Chemical Education
The equilibrium position of a chemical system is based on two distinct considerations, namely, the entropy and enthalpy differences between the states. Loaded dice provide a physical system for…
Bargaining with entropy and energy
This work predicts thermalization of a non-equilibrium statistical system employing the axiom of affine covariance related to the freedom of changing initial points and dimensions for entropy and energy together with the contraction invariance of the entropy-energy diagram.
Observational nonidentifiability, generalized likelihood and free energy
- MathematicsInt. J. Approx. Reason.
Geometric probability theory and Jaynes’s methodology
We provide a generalization of the approach to geometric probability advanced by the great mathematician Gian Carlo Rota, in order to apply it to generalized probabilistic physical theories. In…
SHOWING 1-10 OF 16 REFERENCES
What is Probability
Probabilities may be subjective or objective; we are concerned with both kinds of probability, and the relationship between them. The fundamental theory of objective probability is quantum mechanics:…
Updating, supposing, and maxent
ConclusionThe philosophical controversy concerning the logical status of MAXENTmay be in large measure due to the conflation of two distinct logical roles:(1) A general inductive principle for…
The constraint rule of the maximum entropy principle
- Computer Science
Maximum entropy and Bayesian data analysis: Entropic prior distributions.
- Computer SciencePhysical review. E, Statistical, nonlinear, and soft matter physics
The method of maximum (relative) entropy (ME) is used to translate the information contained in the known form of the likelihood into a prior distribution for Bayesian inference.
Some random observations
ConclusionOf course, the rationale of PME is so different from what has been taught in “orthodox” statistics courses for fifty years, that it causes conceptual hangups for many with conventional…
Jaynes's maximum entropy prescription and probability theory
Jaynes's prescription of maximizing the information-theoretic entropy is applied in a special situation to determine a certain set of posterior probabilities (when evidence fixing the expected value…
Information Theory and Statistical Mechanics
Treatment of the predictive aspect of statistical mechanics as a form of statistical inference is extended to the density-matrix formalism and applied to a discussion of the relation between…
On the relation between plausibility logic and the maximum-entropy principle: a numerical study
A numerical collection of plausibility distributions given by the maximum-entropy principle and by plausibility logic for a set of fifteen simple problems: throwing dice.