The Paradox of the Well-Calibrated Bayesian Forecaster

The well-calibrated Bayesian [pdf]

I explore how a coherent Bayesian forecaster expects to be perfectly calibrated in the long run, meaning their predicted probabilities match actual frequencies. This expectation creates a paradoxical conflict when observed data deviates significantly from predictions, challenging the foundational theory of coherence in subjective probability and weather forecasting.

"We prove a theorem to the effect that a coherent Bayesian expects to be well calibrated, and consider its destructive implications for the theory of coherence."