When an SPF is estimated with a very low overdispersion parameter, which is true in an empirical Bayes estimate of expected crashes?

• A. More weight on observed crashes
• B. More weight on predicted crashes
• C. Equal weight
• D. SPF is not used

Answer: (B)

Empirical Bayes combines the SPF’s predicted crashes with the actual observed crashes, and it does so by weighting each source according to how precise or reliable it is. A very low overdispersion parameter means there’s little extra variability beyond what the model expects, so the observed counts are tightly aligned with the SPF. In that case, the SPF becomes the more informative source, and the posterior estimate leans toward the predicted crashes, giving more weight to them. If overdispersion were higher, the data would be less reliable, and the observed crashes would carry more influence.