Statistical Physics of Group Testing

TL;DR

This paper introduces the application of statistical physics to group testing, focusing on optimal pool design and defect detection inference, with insights relevant to medical and biological testing.

Contribution

It reviews the statistical physics formulation of group testing, highlighting optimal pool design and inference methods, based on prior theoretical work.

Findings

Analysis of optimal pool configurations

Insights into inference algorithms for defect detection

Connections between physics models and testing efficiency

Abstract

This paper provides a short introduction to the group testing problem, and reviews various aspects of its statistical physics formulation. Two main issues are discussed: the optimal design of pools used in a two-stage testing experiment, like the one often used in medical or biological applications, and the inference problem of detecting defective items based on pool diagnosis. The paper is largely based on: M. M\'ezard and C. Toninelli, arXiv:0706.3104, and M. M\'ezard and M. Tarzia {\it Phys. Rev. E} {\bf 76}, 041124 (2007).