A signal detection framework for the evaluation of probabilistic forecasts

In this paper I formulate an approach for evaluating probabilistic forecasts in terms of signal detection theory. Signal detection theory provides a powerful perspective for this type of problem, and a rich empirical background including methodological tools as well as an extensive body of research in many domains. I propose procedures which emphasize the maximization of expected utility for the decision maker who uses the forecasts. Further, I suggest approaches to obtaining indices of calibration and resolution within this framework. I also present arguments that the proposed indices will exhibit the same basic properties as do decompositions of Brier's (1950, Monthly Weather Review, 78, 1-3) mean probability score. However, the properties may be reflected in different ways, and hence, the present methods may lead to different conclusions about forecasting ability. Finally, I argue that the use of an expected utility loss function makes this approach more appropriate for practical applications as well as for theoretical research than other procedures with more arbitrary loss functions.