Monitoring a sequence of Bernoulli random variables subject to gradual changes in the success rates where the success rates are unknown

We look at a sequence of Bernoulli random variables where the success rates change from θ 1 to θ 2 . We will assume that both the success rates before and after the change are unknown but increasing. We assume that this change does not happen abruptly but gradually over a period of time η where η is...

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Bibliographic Details
Published inSequential analysis Vol. 43; no. 2; pp. 233 - 247
Main Author Brown, Marlo
Format Journal Article
LanguageEnglish
Published Philadelphia Taylor & Francis 02.04.2024
Taylor & Francis Ltd
Subjects
Bayesian stopping rules
Bernoulli Hypothesis
change point detection
dynamic programming
False alarms
gradual changes
Random variables
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Summary:We look at a sequence of Bernoulli random variables where the success rates change from θ 1 to θ 2 . We will assume that both the success rates before and after the change are unknown but increasing. We assume that this change does not happen abruptly but gradually over a period of time η where η is known. We calculate the probability that the change has started and completed. We also look at optimal stopping rules assuming that there is a cost for a false alarm and a cost per time unit to stop late.
Bibliography:ObjectType-Article-1
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ISSN:0747-4946
1532-4176
DOI:10.1080/07474946.2024.2338287