TL;DR
This paper demonstrates that calibration failure is a typical and common issue for forecasting systems, contrasting with Bayesian forecasters' confidence in their calibration, raising questions about Bayesian rationality.
Contribution
It extends previous results by showing calibration failure is topologically typical, emphasizing the disconnect between Bayesian beliefs and calibration reality.
Findings
Calibration failure is topologically typical for forecasting systems.
Bayesian forecasters are often certain of their calibration despite widespread failure.
Calibration failure is a common phenomenon across data sequences.
Abstract
Schervish (1985b) showed that every forecasting system is noncalibrated for uncountably many data sequences that it might see. This result is strengthened here: from a topological point of view, failure of calibration is typical and calibration rare. Meanwhile, Bayesian forecasters are certain that they are calibrated---this invites worries about the connection between Bayesianism and rationality.
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Taxonomy
TopicsComplex Systems and Time Series Analysis · Forecasting Techniques and Applications · Reservoir Engineering and Simulation Methods