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The multi-Bayesian sequential decision procedure. (English) Zbl 0611.62003

The methods of S. Weerahandi and J. V. Zidek [Ann. Stat. 11, 1032-1046 (1983; Zbl 0574.62001); see also J. R. Stat. Soc., Ser. A 144, 85-93 (1981; Zbl 0454.62008)] for finding multi-Bayesian decision rules, based on the Kalai-Nash product, can be applied to a situation where there are, at most, M observations taken sequentially. Each Bayesian’s utility for stopping and taking a decision, or continuing to take observations, after n have been taken, can be calculated recursively from the Bayesian’s utilities for group decisions that would be made after \(n+1\) observations. These utilities can then be used with the Kalai-Nash product to find group decisions after n observations. Hence, working backwards, the entire group decision rule can be found. An example is given.

MSC:

62C10 Bayesian problems; characterization of Bayes procedures
62C25 Compound decision problems in statistical decision theory
62L99 Sequential statistical methods
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