# Odds -theorem and monotonicity

Mathematica Applicanda (2019)

- Volume: 47, Issue: 1
- ISSN: 1730-2668

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topF. Thomas Bruss. "Odds -theorem and monotonicity." Mathematica Applicanda 47.1 (2019): null. <http://eudml.org/doc/295491>.

@article{F2019,

abstract = {Given a finite sequence of events and a well-defined notion of events being interesting, the Odds-theorem (Bruss(2000)) gives an online strategy to stop on the last interesting event. This strategy is optimal for independent events, and it is obtained in a straightforward way by an algorithm which is optimal itself (odds-algorithm). Here we study questions in how far the optimal value mirrors monotonicity properties of the underlying sequence of probabilities of events. We make these questions precise, motivate them, and then give complete answers. The motivation is enhanced by certain problems where it seems desirable to apply the odds-algorithm but where a lack of information does not allow to do so without incorporating sequential estimation. In view of this goal, the notion of a plug-in odds-algorithm is introduced. Several applications are included.},

author = {F. Thomas Bruss},

journal = {Mathematica Applicanda},

keywords = {Odds-algorithm; Secretary problem; Selection criteria; Multiple stopping problems; Group interviews; Games; Clinical trial; Prophet inequality},

language = {eng},

number = {1},

pages = {null},

title = {Odds -theorem and monotonicity},

url = {http://eudml.org/doc/295491},

volume = {47},

year = {2019},

}

TY - JOUR

AU - F. Thomas Bruss

TI - Odds -theorem and monotonicity

JO - Mathematica Applicanda

PY - 2019

VL - 47

IS - 1

SP - null

AB - Given a finite sequence of events and a well-defined notion of events being interesting, the Odds-theorem (Bruss(2000)) gives an online strategy to stop on the last interesting event. This strategy is optimal for independent events, and it is obtained in a straightforward way by an algorithm which is optimal itself (odds-algorithm). Here we study questions in how far the optimal value mirrors monotonicity properties of the underlying sequence of probabilities of events. We make these questions precise, motivate them, and then give complete answers. The motivation is enhanced by certain problems where it seems desirable to apply the odds-algorithm but where a lack of information does not allow to do so without incorporating sequential estimation. In view of this goal, the notion of a plug-in odds-algorithm is introduced. Several applications are included.

LA - eng

KW - Odds-algorithm; Secretary problem; Selection criteria; Multiple stopping problems; Group interviews; Games; Clinical trial; Prophet inequality

UR - http://eudml.org/doc/295491

ER -

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