Utility Based Model Selection and Model Averaging

Seminar | November 20 | 3:10-4 p.m. | 1011 Evans Hall

 Jan Vecer, Charles University in Prague

 Department of Statistics

This talk connects several basic concepts from probability, statistics and economic theory. We study model prediction in the form of a distributional opinion about a random variable X and show how to test this prediction against alternative views. Different model opinions can be traded on a hypothetical market that trades their differences. Using a utility maximization technique, we describe such a market for any general random variable X and any utility function U. We specify the optimal behavior of agents and the total market that aggregates all available opinions and show that a correct distributional opinion realizes profit in expectation against any other opinion, giving a novel technique for model selection. The expected profit from this trading defines statistical divergence. In particular, exponential utility gives divergence that is very close to Kullback-Leibler and the logarithmic utility gives a novel f-divergence. Analytical solutions are available for random variables from the exponential family. We also determine the distribution corresponding to the aggregated view of all available opinions, giving a novel technique for model averaging.