Optimal stopping strategies for information purchase in multiple-stage inference tasks

Abstract W. Edwards ( Journal of Mathematical Psychology , 1965 , 2 , 312–329) advanced a solution to the single-stage optional-stopping problem; by using dynamic programming techniques, A. Rapoport and G. J. Burkheimer ( Journal of Mathematical Psychology , 1971 , 8 , 508–538) were able to deal with a broader class of problems. This paper extends Edwards' solution of the optional stopping problem to situations for which input data are uncertain by treating these problems as multiple-stage inference tasks and applying modified Bayes' theorem (MBT). Examined are tasks for which an intermediate stage is fixed and tasks for which an intermediate stage is variable. Also presented is a technique for solving single-stage and multiple-stage problems based on state-dependent cost functions.

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