Template:Did you know nominations/Randomised decision rule

Randomised decision rule

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• ... that a randomised decision rule is sometimes needed to satisfy decision-theoretic criteria such as minimaxity? Young and Smith: Randomised decision rules may appear to be artificial, but minimax solutions may well be of this form.
  • ALT1:... that under some decision-theoretic criteria such as minimax, choosing a decision at random is sometimes optimal? Young and Smith: Randomised decision rules may appear to be artificial, but minimax solutions may well be of this form.
  • ALT2:... that in the past, some statisticians believed randomising statistical decisions under certain situations to be a promising technique? http://projecteuclid.org/euclid.ss/1137076653.
  • ALT3:... that randomised decision rules are sometimes required in the frequentist statistical paradigm but never in the Bayesian one? Robert, p.66: Randomized estimators are nonetheless necessary from a frequentist point of view, for instance, for the frequentist theory of tests, as they provide access to confidence levels otherwise unattainable (see Chapter 5). The set D∗ thus appears as a completion of D. However, this modification of the decision space does not modify the Bayesian answers, as shown by the following result
  • ALT4:... that a randomised decision rule satisfying the Bayes criterion always has a deterministic alternantive? Bickel and Doksum, p.31: For any prior there is always a nonrandomized Bayes procedure, if there is a randomized one.

• Reviewed: Porco (caldera)
• Comment: ALT1 and ALT2 are WP:IARs; I can't think of any way to make the concept more accessible to a broad audience without breaking the rules.

Created/expanded by Kayau (talk). Self-nominated at 04:13, 2 July 2017 (UTC).