An epistemological model of rational decision making, developed by Issac Levi, is applied to the estimation problem. The estimators thus developed are optimal with respect to an epistemic utility function that accounts for the cost of error, the decision agent’s assessment of informational value, and the decision agent’s specified willingness to risk errors in exchange for information acquisition; the estimators are inherently set-valued. Levi’s stable acceptance procedure is applied to the estimation process, facilitating the use of unnormalized probability densities. The convergence of the stable acceptance process is proven and it is shown that it results in a classical MAP estimator as a special case. A representation theorem is also proven that makes computation of the estimates possible. Two examples are provided to illustrate the theory.
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