Nonlinearity conjecture for false confidence

Prove or refute the conjecture that false confidence tends to occur when hypotheses concern the values of non-linear functions of the model parameters, thereby establishing whether nonlinearity is a principal driver of unreliability in probabilistic uncertainty quantification.

Background

Following the presentation of the false confidence theorem, the author hypothesizes that nonlinearity in the mapping from parameters to hypotheses is a key factor behind false confidence. Examples and related analyses hint at this pattern but do not establish it rigorously.

A formal resolution of this conjecture would clarify when probabilistic methods (e.g., Bayesian posteriors) are prone to misleading certainty, guiding both theory and practice.