  Point estimation is a fundamental statistical task. Given the wide selection
of available point estimators, it is unclear, however, what, if any, would be
universally-agreed theoretical reasons to generally prefer one such estimator
over another. In this paper, we define a class of estimation scenarios which
includes commonly-encountered problem situations such as both ``high stakes''
estimation and scientific inference, and introduce a new class of estimators,
Error Intolerance Candidates (EIC) estimators, which we prove is optimal for
it.
  EIC estimators are parameterised by an externally-given loss function. We
prove, however, that even without such a loss function if one accepts a small
number of incontrovertible-seeming assumptions regarding what constitutes a
reasonable loss function, the optimal EIC estimator can be characterised
uniquely.
  The optimal estimator derived in this second case is a previously-studied
combination of maximum a posteriori (MAP) estimation and Wallace-Freeman (WF)
estimation which has long been advocated among Minimum Message Length (MML)
researchers, where it is derived as an approximation to the
information-theoretic Strict MML estimator. Our results provide a novel
justification for it that is purely Bayesian and requires neither
approximations nor coding, placing both MAP and WF as special cases in the
larger class of EIC estimators.
