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We define a new class of Bayesian point estimators, which we refer to as riskaverse. Using this definition, we formulate axioms that provide naturalrequirements for inference, e.g. in a scientific setting, and show that forwell-behaved estimation problems the axioms uniquely characterise an estimator.Namely, for estimation problems in which some parameter values have a positiveposterior probability (such as, e.g., problems with a discrete hypothesisspace), the axioms characterise Maximum A Posteriori (MAP) estimation, whereaselsewhere (such as in continuous estimation) they characterise theWallace-Freeman estimator.  Our results provide a novel justification for the Wallace-Freeman estimator,which previously was derived only as an approximation to theinformation-theoretic Strict Minimum Message Length estimator. By contrast, ourderivation requires neither approximations nor coding.

Risk-averse estimation, an axiomatic approach to inference, and Wallace-Freeman without MML