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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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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Abstract 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.
AbstractList 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.
We look at a sequence of Bernoulli random variables where the success rates change from θ1 to θ2. 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.
Author Brown, Marlo
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10.1111/j.1467-9469.2004.02-102.x
10.1214/14-AOS1297
10.1016/B978-0-12-589320-6.50016-2
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Snippet 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...
We look at a sequence of Bernoulli random variables where the success rates change from θ1 to θ2. We will assume that both the success rates before and after...
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StartPage 233
SubjectTerms Bayesian stopping rules
Bernoulli Hypothesis
change point detection
dynamic programming
False alarms
gradual changes
Random variables
Title Monitoring a sequence of Bernoulli random variables subject to gradual changes in the success rates where the success rates are unknown
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Volume 43
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