Aggregation of Non-Binary Predictions

Combining several predictions from several forecasters or models consistently improves the accuracy of forecasts. Methods may differ depending on whether forecasts are for a binary (yes/no) or a non-binary target (like world GDP in year X). This page only deals with aggregating probabilistic forecasts (i.e. predictive distributions) for non-binary outcomes. Aggregation techniques for binary forecasts can be found here.

Ways of combining probability distributions


Probability distributions can be combined either based on their probability density functions (PDF) or their cumulative density functions (CDF). Usually, forecasts are combined using the CDF. CDF can be either combined horizontally or vertically.

A horizontal combination of several CDF is equal to a combination of the quantiles of the CDF. A vertical combination of the CDF is equal to a mixture distribution that combines the cumulative densities of the individual forecasts.