Utility Based Model Selection and Model Averaging

This paper presents a novel approach to model selection and model averaging based on economic theory. We study model prediction in the form of a distributional opinion about a random variable X. We 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. Analytical solutions are available for random variables from the exponential family. We determine the distribution corresponding to the aggregated view of all available opinions, giving a novel technique for model averaging