  Bayesian error analysis paves the way to the construction of credible and
plausible error regions for a point estimator obtained from a given dataset. We
introduce the concept of region accuracy for error regions (a generalization of
the point-estimator mean squared-error) to quantify the average statistical
accuracy of all region points with respect to the unknown true parameter. We
show that the increase in region accuracy is closely related to the
Bayesian-region dual operations in [1]. Next with only the given dataset as
viable evidence, we establish various adaptive methods to maximize the region
accuracy relative to the true parameter subject to the type of reported
Bayesian region for a given point estimator. We highlight the performance of
these adaptive methods by comparing them with nonadaptive procedures in three
quantum-parameter estimation examples. The results of and mechanisms behind the
adaptive schemes can be understood as the region analog of adaptive approaches
to achieving the quantum Cramer--Rao bound for point estimators.
