Volume 26, 2020
|Number of page(s)||26|
|Published online||03 September 2020|
Bayesian sequential testing with expectation constraints*
Institute for Mathematics, University of Jena,
2 TU Wien, Institute of Statistics and Mathematical Methods in Economics, Wiedner Hauptstr. 8 / E105-1 & -5 FAM, 1040 Wien, Austria.
** Corresponding author: email@example.com
Accepted: 15 July 2019
We study a stopping problem arising from a sequential testing of two simple hypotheses H0 and H1 on the drift rate of a Brownian motion. We impose an expectation constraint on the stopping rules allowed and show that an optimal stopping rule satisfying the constraint can be found among the rules of the following type: stop if the posterior probability for H1 attains a given lower or upper barrier; or stop if the posterior probability comes back to a fixed intermediate point after a sufficiently large excursion. Stopping at the intermediate point means that the testing is abandoned without accepting H0 or H1. In contrast to the unconstrained case, optimal stopping rules, in general, cannot be found among interval exit times. Thus, optimal stopping rules in the constrained case qualitatively differ from optimal rules in the unconstrained case.
Mathematics Subject Classification: 62L10 / 60G40 / 62L15
Key words: Bayesian sequential testing / optimal stopping / expectation constraint
© EDP Sciences, SMAI 2020
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