Optimum Detection of Defective Elements in Non-Adaptive Group Testing

TL;DR

This paper develops an efficient method using trellis representation to compute posterior defect probabilities in non-adaptive group testing, applicable to both noiseless and noisy models, with analysis of complexity and error trade-offs.

Contribution

It introduces a novel trellis-based technique for posterior probability computation in non-adaptive group testing, handling noise and complexity considerations.

Findings

Effective for moderate-sized populations

Balances false positive and false negative probabilities

Applicable to both noiseless and noisy testing models

Abstract

We explore the problem of deriving a posteriori probabilities of being defective for the members of a population in the non-adaptive group testing framework. Both noiseless and noisy testing models are addressed. The technique, which relies of a trellis representation of the test constraints, can be applied efficiently to moderate-size populations. The complexity of the approach is discussed and numerical results on the false positive probability vs. false negative probability trade-off are presented.