John D. Cook • 4/4/2026

Kalman and Bayes average grades

This article explores the simple problem of updating an average grade as a special case of Bayesian statistics and Kalman filtering. It shows how the new average can be computed from the previous average and the new grade using a weighted average, with weights based on the number of grades. The author derives formulas for the new mean as a compromise between prior and new data, and relates it to the Kalman filter gain. The post connects these concepts to sufficient statistics, Bayesian updating with a normal likelihood and flat prior, and links to related posts on Bayesian views and Kalman filters.

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#Bayesian Statistics #Kalman Filter #Average Grade