Bayesian Inference and the Principle of Maximum Entropy

Duncan Foley and Ellis Scharfenaker

Working Paper Series, Department of Economics, University of Utah from University of Utah, Department of Economics

Abstract: Bayes' theorem incorporates distinct types of information through the likelihood and prior. Direct observations of state variables enter the likelihood and modify posterior probabilities through consistent updating. Information in terms of expected values of state variables modify posterior probabilities by constraining prior probabilities to be consistent with the information. Constraints on the prior can be exact, limiting hypothetical frequency distributions to only those that satisfy the constraints, or be approximate, allowing residual deviations from the exact constraint to some degree of tolerance. When the model parameters and constraint tolerances are known, posterior probability follows directly from Bayes' theorem. When parameters and tolerances are unknown a prior for them must be specified. When the system is close to statistical equilibrium the computation of posterior probabilities is simplified due to the concentration of the prior on the maximum entropy hypothesis. The relationship between maximum entropy reasoning and Bayes' theorem from this point of view is that maximum entropy reasoning is a special case of Bayesian inference with a constrained entropy-favoring prior.

Keywords: Bayesian inference; Maximum entropy; Priors; Information theory; Statistical equilibrium JEL Classification: (search for similar items in EconPapers)
Pages: 21 Pages
Date: 2024
New Economics Papers: this item is included in nep-ecm and nep-mic
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Persistent link: https://EconPapers.repec.org/RePEc:uta:papers:2024-03

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