Decision Theoretic Cutoff and ROC Analysis for Bayesian Optimal Group Testing
Abstract
We study the inference problem in the group testing to identify defective items from the perspective of the decision theory. We introduce Bayesian inference and consider the Bayesian optimal setting in which the true generative process of the test results is known. We demonstrate the adequacy of the posterior marginal probability in the Bayesian optimal setting as a diagnostic variable based on the area under the curve (AUC). Using the posterior marginal probability, we derive the general expression of the optimal cutoff value that yields the minimum expected risk function. Furthermore, we evaluate the performance of the Bayesian group testing without knowing the true states of the items: defective or nondefective. By introducing an analytical method from statistical physics, we derive the receiver operating characteristics curve, and quantify the corresponding AUC under the Bayesian optimal setting. The obtained analytical results precisely describes the actual performance of the belief propagation algorithm defined for single samples when the number of items is sufficiently large.
 Publication:

arXiv eprints
 Pub Date:
 October 2021
 arXiv:
 arXiv:2110.10877
 Bibcode:
 2021arXiv211010877S
 Keywords:

 Computer Science  Information Theory;
 Condensed Matter  Disordered Systems and Neural Networks
 EPrint:
 17 pages, 8 figures