Decision Theoretic Cutoff and ROC Analysis for Bayesian Optimal Group Testing

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