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A negative binomial approximation in group testing

Part of: Distribution theory Communication, information Limit theorems

Published online by Cambridge University Press:  28 October 2022

Letian Yu ,
Fraser Daly  and
Oliver Johnson Open the ORCID record for Oliver Johnson [Opens in a new window]
Letian Yu
Affiliation:
Department of System Engineering and Engineering Management, The Chinese University of Hong Kong, Shatin NT, Hong Kong. E-mail: letian.yu@link.cuhk.edu.hk
Fraser Daly
Affiliation:
Department of Actuarial Mathematics and Statistics, Heriot–Watt University, Edinburgh EH14 4AS, UK. E-mail: f.daly@hw.ac.uk
Oliver Johnson
Affiliation:
School of Mathematics, University of Bristol, Fry Building, Woodland Road, Bristol BS8 1UG, UK. E-mail: o.johnson@bristol.ac.uk
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Abstract

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.

Keywords

Group testingPooled testingStein–Chen method

MSC classification

Primary: 62E17: Approximations to distributions (nonasymptotic)
Secondary: 60F05: Central limit and other weak theorems 94A20: Sampling theory
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 37 , Issue 4 , October 2023 , pp. 973 - 996
Copyright
© The Author(s), 2022. Published by Cambridge University Press

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