Author: Junan Zhu; Kristina Rivera; Dror Baron
Title: Noisy Pooled PCR for Virus Testing Document date: 2020_4_8
ID: 8kccpd4x_21
Snippet: We now account for these false positives and negatives. The noisy measurement y m depends on w m through a conditional probability, Pr(Y m |W m ), where Y m and W m are RVs. To evaluate Pr(Y m |W m ), we denote the probability of an individual patient being sick yet not having enough genetic material in one of the measurements by p 1 . This is the probability of a false negative caused by one patient; with w m sick patients, the probability that .....
Document: We now account for these false positives and negatives. The noisy measurement y m depends on w m through a conditional probability, Pr(Y m |W m ), where Y m and W m are RVs. To evaluate Pr(Y m |W m ), we denote the probability of an individual patient being sick yet not having enough genetic material in one of the measurements by p 1 . This is the probability of a false negative caused by one patient; with w m sick patients, the probability that all of them have false negatives is (p 1 ) wm . (We note in passing that false negatives could be modeled as independent of w m [3] .)
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