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arXiv 2004.136672020-04stat.MLcond-mat.dis-nncs.LG

Bayesian inference of infected patients in group testing with prevalence estimation

Institute of Statistical Mathematics（统计数理研究所）；The Graduate University for Advanced Science (SOKENDAI)（综合研究大学院大学）

Ayaka Sakata

DOI：: 10.7566/JPSJ.89.084001

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Group testing is a method of identifying infected patients by performing tests on a pool of specimens collected from patients. For the case in which the test returns a false result with finite probability, we propose Bayesian inference and a corresponding belief propagation (BP) algorithm to identify the infected patients from the results of tests performed on the pool. We show that the true-positive rate is improved by taking into account the credible interval of a point estimate of each patient. Further, the prevalence and the error probability in the test are estimated by combining an expectation-maximization method with the BP algorithm. As another approach, we introduce a hierarchical Bayes model to identify the infected patients and estimate the prevalence. By comparing these methods, we formulate a guide for practical usage.

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