A negative binomial approximation in group testing

TL;DR

This paper models the distribution of intruding items in non-adaptive group testing using a negative binomial approximation, enhancing understanding of algorithm performance and error analysis.

Contribution

It introduces a negative binomial approximation for intruding items in Bernoulli-designed group testing, aiding performance evaluation of specific algorithms.

Findings

Negative binomial distribution closely approximates intruding item count

Improved understanding of error probabilities in group testing algorithms

Enhanced analysis of the two-stage conservative group testing method

Abstract

We consider the problem of group testing (pooled testing), first introduced by Dorfman. For non-adaptive testing strategies, we refer to a non-defective item as `intruding' if it only appears in positive tests. Such items cause mis-classification 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.