Partial Information Framework: Basic Theory and Applications

PARTIAL INFORMATION FRAMEWORK: BASIC THEORY AND APPLICATIONS Ville A. Satopää Shane T. Jensen Lyle H. Ungar Many real-world decisions depend on accurate predictions of some future outcome. In such cases the decision-maker often seeks to consult multiple people or/and models for their forecasts. These forecasts are then aggregated into a consensus that is inputted in the final decision-making process. Principled aggregation requires an understanding of why the forecasts are different. Historically, such forecast heterogeneity has been explained by measurement error. This dissertation, however, first shows that measurement error is not appropriate for modeling forecast heterogeneity and then introduces information diversity as a more appropriate yet fundamentally different alternative. Under information diversity differences in the forecasts stem purely from differences in the information that is used in the forecasts. This is made mathematically precise in a new modeling framework called the partial information framework. At its most general level, the partial information framework is a very reasonable model of multiple forecasts and hence offers an ideal platform for theoretical analysis. For one, it explains the empirical phenomenon known as extremization. This is a popular technique that often improves the out-of-sample performance of simple aggregators, such as the average or median, by transforming them directly away from the marginal mean of the outcome. Unfortunately, the general framework is too abstract for practical applications. To apply the framework in practice one needs to choose a parametric distribution for the forecasts and outcome. This dissertation motivates and chooses the multivariate Gaussian distribution. The result, known as the Gaussian partial information model, is a very close yet practical specification of the framework. The optimal aggregator under the Gaussian model is shown to outperform the state-of-the-art measurement error aggregators on both synthetic and many different types of real-world forecasts.