A note on the aggregation of event probabilities

Area of Science:

• Statistics
• Probability Theory
• Decision Making

Background:

• Recent research increasingly utilizes large numbers of individual forecasts for event probability estimation.
• Aggregating diverse probabilistic forecasts presents a significant analytical challenge.

Purpose of the Study:

• To develop a method for aggregating multiple probabilistic forecasts.
• To examine the theoretical properties of aggregated forecasts under specific assumptions.

Main Methods:

• Forecasts treated as data and aggregated using Bayes' theorem.
• Assumptions of calibration and conditional independence applied to forecast aggregation.
• Development of a measure of discrimination for evaluating forecast quality.

Main Results:

• A Bayesian framework for aggregating probabilistic forecasts is established.
• The behavior of aggregated posterior probability is analyzed with increasing numbers of forecasters.
• A discrimination measure is provided for assessing forecast performance.

Conclusions:

• The proposed aggregation method provides a robust approach for combining probabilistic forecasts.
• The study offers insights into the statistical properties of aggregated forecasts in large-scale forecasting scenarios.