Admissible Decision Rule

What is the Admissible Decision Rule?

The admissible decision rule is a function for deciding which available course of action always generates the best result. This doesn’t mean the decision is truly the optimal solution to a problem, just that it is the most dominant (admissible) decision rule among all the currently available courses of action. The specific process for determining admissibility varies depending on what probability model is employed, either Frequentist or Bayesian.

What’s the Difference Between Frequentist and Bayesian Decision Rules?

In the Frequentist (classical statistics) model, the goal is to choose the decision rule that has the best balance between the loss function (cost) and expectation function (risk), in relation to all the other possible decisions. 

In this approach, the states of nature, such as the data sample’s range and constraints, as well as the risk function are considered fixed and constant.

In Bayesian probability though, both the data’s nature and the risk function are defined by a range of probabilities (expectations) that need to be chosen before the best decision rule can be calculated. This prior probability can be chosen from past models, experiments, some general principle such as maximizing entropy or just a subjective human assessment. When absolutely no information is available, an uninformative prior probability can be created that reflects a balance among outcomes.