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Group testing is the process of pooling samples (e.g., blood, chemical compounds) from multiple sources and testing the pooled material for some binary characteristic. It is used in pathogen screening for humans and animals, drug discovery studies, electrical systems testing, and many other applications. Group testing has traditionally been used for two main types of investigations: 1) the identification of positive specimens and 2) the estimation of a characteristic’s prevalence in a population. This dissertation focuses on the identification process. We propose new identification procedures that exploit the heterogeneity among samples in order to reduce the number of tests needed to detect the binary characteristic. We first propose the “ordered halving” procedure which is shown to reduce the expected number of tests in comparison to current implementations of halving. Next, we generalize our proposals to a class of hierarchical group testing procedures. Our proposals result in significant reductions in the expected number of tests while also maintaining accuracy at levels similar to those procedures which do not account for heterogeneity.
Advisor: Christopher R. Bilder