Applications of the divergence theorem in Bayesian inference and MaxEnt

Abstract

Given a probability density $P(\mathbf{x}|\mathbf{\lambda })$, where $\mathbf{x}$ represents continuous degrees of freedom and $\lambda$ a set of parameters, it is possible to construct a general identity relating expectations of observable quantities, which is a generalization of the equipartition theorem in Thermodynamics. In this work we explore some of the consequences of this relation, both in the context of sampling distributions and Bayesian posteriors, and how it can be used to extract some information without the need for explicit calculation of the partition function (or the Bayesian evidence, in the case of posterior expectations). Together with the general family of fluctuation theorems it constitutes a powerful tool for Bayesian/MaxEnt problems.

References in corpus (3)

• Updating Probabilities
• Hamiltonian formalism and path entropy maximization
• Newtonian Dynamics from the principle of Maximum Caliber

Cited by in corpus (8)

• Fluctuating temperature outside superstatistics: thermodynamics of small systems
• Ensemble-free configurational temperature for spin systems
• Kappa distribution from particle correlations in non-equilibrium, steady-state plasmas
• Computational Statistical Mechanics of a confined, three-dimensional Coulomb gas
• Superstatistics as the thermodynamic limit of driven classical systems
• Fundamental temperature exclusively determines the validity of superstatistics
• A classification of nonequilibrium steady states based on temperature correlations
• Fluctuation theorems in nonextensive statistics