Sigma Club Seminar by Ellis Scharfenaker (University of Utah)

Title: Bayes’ Theorem and the Principle of Maximum Entropy.

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 probabilities follow 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.

Ellis Scharfenaker is an Assistant Professor of Economics at the University of Utah. His research develops the statistical and theoretical foundations necessary to understand how the complex interactions of heterogeneous agents, mediated by economic and social institutions, generate observable macroeconomic distributional patterns. Drawing on insights from information theory, statistical mechanics, and Bayesian inference, his work focuses on the stochastic generative dynamics of distributional outcomes in income, wealth, profit, output, and growth.

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