Evaluating and Analyzing Probabilistic Forecasts (UMAP)

This module presents an analysis of the quality of probabilistic forecasts, such as weather forecasting and sporting events. It describes both discrete and continuous forecasts using graphical indicators. Reliability diagrams and covariance graphs are introduced. A variety of forecasting methods are evaluated.

Table of Contents:

1. INTRODUCTION
1.1 Some Practical Decision Problems
1.2 The Issue: Probabilistic Forecast Quality

2. METHODS FOR DISCRETE FORECASTS
2.1 Situations and Notation
2.2 Graphical Indicators of Forecast Characterstics - Calibration-in-the-Small and Resolution
2.3 The Probability Score and Its Mean
2.4 The Sanders Decomposition of the Mean Probability Score
2.5 The Murphy Decomposition of the Mean Probability Score
2.6 Some Real Examples: Weather and Baseball

3. METHODS FOR CONTINUOUS FORECASTS
3.1 Situations and Notation
3.2 Graphical Indicators of Forecast Characteristics - Calibration-in-the-Large, Slope, Scatter, Conditional Distributions
3.3 The Probability Score for Continuous Forecasts and the Covariance Decomposition of Its Mean
3.4 Weather and Baseball Revisited
3.5 Relationships Among the Decompositions of PS

4. PROPERNESS: A SPECIAL PROPERTY OF THE PROBABILITY SCORE

5. BIBLIOGRAPHY

6. EXERCISES

7. ANSWERS TO EXERCISES