A negative binomial approximation in group testing

Letian Yu, Fraser A. Daly, Oliver Johnson*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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We consider the problem of group testing (pooled testing), first introduced by Dorfman. For nonadaptive testing strategies, we refer to a nondefective item as “intruding” if it only appears in positive tests. Such items cause misclassification errors in the well-known COMP algorithm and can make other algorithms produce an error. It is therefore of interest to understand the distribution of the number of intruding items. We show that, under Bernoulli matrix designs, this distribution is well approximated in a variety of senses by a negative binomial distribution, allowing us to understand the performance of the two-stage conservative group testing algorithm of Aldridge.
Original languageEnglish
Pages (from-to)973-996
Number of pages24
JournalProbability in the Engineering and Informational Sciences
Issue number4
Early online date28 Oct 2022
Publication statusPublished - Oct 2023


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