Statistics and Its Interface

Volume 16 (2023)

Number 4

On the optimal configuration of a square array group testing algorithm

Pages: 579 – 591

DOI: https://dx.doi.org/10.4310/22-SII746

Authors

Ugn Čiżikovienė (Institute of Applied Mathematics, Faculty of Mathematics and Informatics, Vilnius University, Vilnius, Lithuania)

Viktor Skorniakov (Institute of Applied Mathematics, Faculty of Mathematics and Informatics, Vilnius University, Vilnius, Lithuania)

Abstract

Up to date, only lower and upper bounds for the optimal configuration of a Square Array (A2) Group Testing (GT) algorithm are known. We establish exact analytical formulae and provide a couple of applications of our result. First, we compare the A2 GT scheme to several other classical GT schemes in terms of the gain per specimen attained at optimal configuration. Second, operating under objective Bayesian framework with the loss designed to attain minimum at optimal configuration, we suggest the preferred choice of the group size under natural minimal assumptions: the prior information regarding the prevalence suggests that grouping and application of A2 is better than individual testing. The same suggestion is provided for the Minimax strategy.

Keywords

group testing, square array, optimal configuration

2010 Mathematics Subject Classification

Primary 62P10, 62-xx. Secondary 92C50, 92-xx.

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Received 14 November 2021

Accepted 22 June 2022

Published 14 April 2023