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Disorder detection with costly observations

Part of: Sequential methods Parametric inference

Published online by Cambridge University Press:  25 April 2022

Erhan Bayraktar ,
Erik Ekström  and
Jia Guo
Erhan Bayraktar*
Affiliation:
University of Michigan
Erik Ekström*
Affiliation:
Uppsala University
Jia Guo*
Affiliation:
University of Michigan
*
*Postal address: Department of Mathematics, University of Michigan, 530 Church Street, Ann Arbor, MI 48104, USA
***Postal address: Department of Mathematics, Uppsala University, Box 256, 75105 Uppsala, Sweden. Email: ekstrom@math.uu.se
*Postal address: Department of Mathematics, University of Michigan, 530 Church Street, Ann Arbor, MI 48104, USA
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Abstract

We study the Wiener disorder detection problem where each observation is associated with a positive cost. In this setting, a strategy is a pair consisting of a sequence of observation times and a stopping time corresponding to the declaration of disorder. We characterize the minimal cost of the disorder problem with costly observations as the unique fixed point of a certain jump operator, and we determine the optimal strategy.

Keywords

Wiener disorder detectiondiscrete cost of observationoptimal stopping

MSC classification

Primary: 62L10: Sequential analysis
Secondary: 62F15: Bayesian inference 62L15: Optimal stopping
Type
Original Article
Information
Journal of Applied Probability , Volume 59 , Issue 2 , June 2022 , pp. 338 - 349
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Applied Probability Trust

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