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College of Business
AACSB International EQUIS - European Quality Improvement System
Research Seminar
Seminar: Bayes Risk in New Contexts: Mean Excess Error, Gini, Fisher, and Jeffreys
Abstract: This presentation gives an overview of recent developments on the Bayes risk in new contexts such as ranking forecast models by stochastic error distance (SED) proposed by Diebold and Shin (2017), Gini coefficient of income inequality, and expected Fisher information. The mean excess or residual function is the optimal predictor under the quadratic loss of the amount a random variable exceeds a given threshold, which is a function of the threshold, hence a local measure. Its global risk under a distribution for the threshold is the Bayes risk. The mean excess error (MEE) ranks forecast models by only penalizing errors with magnitudes larger than a tolerance threshold. The MEE is within the SED framework as a dynamic extension of the mean absolute error and its Bayes risk is the Shannon entropy functional of the survival function of the absolute error. The Bayes risk of the mean excess of a random variable distributed as the proportional hazards model is a generalized entropy functional of the survival function, which gives the Gini measure as a special case. The Fisher information provided by a random variable about a parameter of its distribution is, in general, a function of the unknown parameter. We define the Bayes Fisher information by the expected Fisher information under a prior for the parameter. We present the Fisher information of the mixture of two probability density functions (PDFs) about the mixing parameter in terms of chi-square divergence between the two PDFs. The Bayes Fisher information of the mixture distribution under the uniform prior for the mixing parameter is the Jeffreys divergence between the two PDFs and under a triangular prior is proportional to the Jensen-Shannon divergence of the mixture.
Date: Dec 4 (Mon), 2017 4:30 pm - 5:30 pm
Time: 4:30PM - 5:30PM
Speaker: Prof Ehsan S. Soofi
University of Wisconsin
Venue: Room 14-221, 14/F, Lau Ming Wai Academic Building