International Journal of Stochastic Analysis
Volume 2012 (2012), Article ID 697458, 8 pages
Research Article

Bayes' Model of the Best-Choice Problem with Disorder

Institute of Applied Mathematical Research, Karelian Research Centre of RAS, IAMR KRC RAS 11, Pushkinskaya Street, Petrozavodsk, Karelia 185910, Russia

Received 10 December 2010; Accepted 21 March 2011

Academic Editor: Onesimo Hernandez Lerma

Copyright © 2012 Vladimir Mazalov and Evgeny Ivashko. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We consider the best-choice problem with disorder and imperfect observation. The decision-maker observes sequentially a known number of i.i.d random variables from a known distribution with the object of choosing the largest. At the random time the distribution law of observations is changed. The random variables cannot be perfectly observed. Each time a random variable is sampled the decision-maker is informed only whether it is greater than or less than some level specified by him. The decision-maker can choose at most one of the observation. The optimal rule is derived in the class of Bayes' strategies.