An equalizer rule has the same risk at every parameter value. A Bayes equalizer rule is minimax when its constant risk bounds from below the worst-case risk of every competing rule.
For two distinct nonsingular Gaussian class distributions, vary the class-zero prior continuously. The class-zero and class-one error probabilities of the corresponding Bayes classifier cross. At a crossing they are equal, making the classifier an equalizer rule, a minimax decision rule, and the associated prior a least favorable prior.
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