Copula Calibration

We propose notions of calibration for probabilistic forecasts of general multivariate quantities. Probabilistic copula calibration is a natural analogue of probabilistic calibration in the univariate setting. It can be assessed empirically by checking for the uniformity of the copula probability integral transform (CopPIT), which is invariant under coordinate permutations and coordinatewise strictly monotone transformations of the predictive distribution and the outcome. The CopPIT histogram can be interpreted as a generalization and variant of the multivariate rank histogram, which has been used to check the calibration of ensemble forecasts. Climatological copula calibration is an analogue of marginal calibration in the univariate setting. Methods and tools are illustrated in a simulation study and applied to compare raw numerical model and statistically postprocessed ensemble forecasts of bivariate wind vectors

Strategic Disclosure of Valuable Information within Competitive Environments

Can valuable information be disclosed intentionally by the informed agent even within a competitive environment? In this article, we bring our interest into the asymmetry in reward and penalty in the payoff structure and explore its effects on the strategic disclosure of valuable information. According to our results, the asymmetry in reward and penalty is a necessary condition for the disclosure of valuable information. This asymmetry also decides which quality of information is revealed for which incentive; if the penalty is larger than the reward or the reward is weakly larger than the penalty, there exists an equilibrium in which only a low quality type of information is revealed, in order to induce imitation. On the other hand, if the reward is sufficiently larger than the penalty, there exist equilibria in which either all types or only high quality type of information is revealed, in order to induce deviation. The evaluation of the equilibrium in terms of expected payoff yields that the equilibrium where valuable information is disclosed strategically dominates the equilibrium where it is concealed.

On the relationship between individual and group decisions

Each member of a group receives a signal about the unknown state of the world and decides on a utility-maximizing recommendation on the basis of that signal. The individuals have identical preferences. The group makes a decision that maximizes the common utility function assuming perfect pooling of the information in individual signals. An action profile is a group action and a recommendation from each individual. A collection of action profiles is rational if there exists an information structure under which all elements in the collection arise with positive probability. With no restrictions on the information structure, essentially all action profiles are rational. In fact, given any distribution over action profiles, it is possible to find an information structure that approximates the distribution. In a monotone environment in which individuals receive conditionally independent signals, essentially any single action profile is rational, although some collections of action profiles are not. © 2014 Joel Sobel

Quantifying the Influences on Probabilistic Wind Power Forecasts

In recent years, probabilistic forecasts techniques were proposed in research as well as in applications to integrate volatile renewable energy resources into the electrical grid. These techniques allow decision makers to take the uncertainty of the prediction into account and, therefore, to devise optimal decisions, e.g., related to costs and risks in the electrical grid. However, it was yet not studied how the input, such as numerical weather predictions, affects the model output of forecasting models in detail. Therefore, we examine the potential influences with techniques from the field of sensitivity analysis on three different black-box models to obtain insights into differences and similarities of these probabilistic models. The analysis shows a considerable number of potential influences in those models depending on, e.g., the predicted probability and the type of model. These effects motivate the need to take various influences into account when models are tested, analyzed, or compared. Nevertheless, results of the sensitivity analysis will allow us to select a model with advantages in the practical application.Comment: 5 pages; 1 table; 3 figures; This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessibl