Random and quasi-random designs in group testing

Noonan, Jack and Zhigljavsky, Anatoly ORCID: https://orcid.org/0000-0003-0630-8279 2022. Random and quasi-random designs in group testing. Journal of Statistical Planning and Inference 221 , pp. 29-54. 10.1016/j.jspi.2022.02.006

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Abstract

For large classes of group testing problems, we derive lower bounds for the probability that all significant items are uniquely identified using specially constructed random designs. These bounds allow us to optimize parameters of the randomization schemes. We also suggest and numerically justify a procedure of constructing designs with better separability properties than pure random designs. We illustrate theoretical considerations with a large simulation-based study. This study indicates, in particular, that in the case of the common binary group testing, the suggested families of designs have better separability than the popular designs constructed from disjunct matrices. We also derive several asymptotic expansions and discuss the situations when the resulting approximations achieve high accuracy.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Publisher:	Elsevier
ISSN:	0378-3758
Date of First Compliant Deposit:	10 March 2022
Date of Acceptance:	23 February 2022
Last Modified:	06 Nov 2023 19:32
URI:	https://orca.cardiff.ac.uk/id/eprint/148049

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