  Results concerning the construction of quantum Bayesian error regions as a
means to certify the quality of parameter point estimators have been reported
in recent years. This task remains numerically formidable in practice for large
dimensions and so far, no analytical expressions of the region size and
credibility (probability of any given true parameter residing in the region)
are known, which form the two principal region properties to be reported
alongside a point estimator obtained from collected data. We first establish
analytical formulas for the size and credibility that are valid for a uniform
prior distribution over parameters, sufficiently large data samples and general
constrained convex parameter-estimation settings. These formulas provide a
means to an efficient asymptotic error certification for parameters of
arbitrary dimensions. Next, we demonstrate the accuracies of these analytical
formulas as compared to numerically computed region quantities with simulated
examples in qubit and qutrit quantum-state tomography where computations of the
latter are feasible.
