A binary search scheme for determining all contaminated specimens

• Main Author: Papanicolaou, V.G (Author)
• Format: Article
• Language: English
• Published: Springer Science and Business Media Deutschland GmbH 2021
• Subjects: Adaptive group testing; Average-case aspect ratio; Binary search scheme; Characteristic function; Limiting distribution; Linear regime; Moments; Normal distribution; prevalence; Prevalence; Prevalence (rate); Probabilistic testing; probability; Probability
• Online Access: View Fulltext in Publisher

 Specimens are collected from N different sources. Each specimen has probability p of being contaminated (in the case of a disease, e.g., p is the prevalence rate), independently of the other specimens. Suppose we can apply group testing, namely take small portions from several specimens, mix them together, and test the mixture for contamination, so that if the test turns positive, then at least one of the samples in the mixture is contaminated. In this paper we give a detailed probabilistic analysis of a binary search scheme, we propose, for determining all contaminated specimens. More precisely, we study the number T(N) of tests required in order to find all the contaminated specimens, if this search scheme is applied. We derive recursive and, in some cases, explicit formulas for the expectation, the variance, and the characteristic function of T(N). Also, we determine the asymptotic behavior of the moments of T(N) as N→ ∞ and from that we obtain the limiting distribution of T(N) (appropriately normalized), which turns out to be normal. © 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.