Lesson plan
Complete class theorem
The Complete class theorems is a class of theorems in decision theory. They establish that all admissible decision rules are equivalent to the Bayesian decision rule for some utility function and some prior distribution (or for the limit of a sequence of prior distributions). Thus, for every decision rule, either the rule may be reformulated as a Bayesian procedure (or a limit of a sequence of such), or there is a rule that is sometimes better and never worse. For example, Ferguson [section 2.10] gives a theorem establishing that if the sample space is closed and the parameter space is finite then the class of Bayes rules is complete.
Article summary
The Complete class theorems is a class of theorems in decision theory. They establish that all admissible decision rules are equivalent to the Bayesian decision rule for some utility function and some prior distribution (or for the limit of a sequence of prior distributions). Thus, for every decision rule, either the rule may be reformulated as a Bayesian procedure (or a limit of a sequence of such), or there is a rule that is sometimes better and never worse. For example, Ferguson [section 2.10] gives a theorem establishing that if the sample space is closed and the parameter space is finite then the class of Bayes rules is complete.
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Discussion questions
- Summarise the article in your own words. Which single claim would you verify first, and why?
- Which claim in this article is most likely to be revised as the sources update? How would you check its current status?
- If two sources disagreed about one of these facts, what would you need in order to trust one over the other?
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