Adaptive Bayesian group testing: Algorithms and performance

Abstract

Abstract Group testing is applied to recover a small defective subset of items by a number of tests much smaller than the total population. In this paper, we study group testing from the Bayesian perspective. The state of all the items is manipulated as a random variable, the probability function of which is updated iteratively. We also propose an algorithm which designs the measurement vectors adaptively to decrease the number of tests, compared to non-adaptive methods. The measurement vector is chosen by maximizing the expectation of update gain in each test. We also propose a fast approximation method, which updates the probability function of each item independently to decrease the computational cost when designing the measurement vector within each test. Furthermore, the expected value of the required numbers of tests for the proposed methods are deduced theoretically. The deduced results are appropriate for both the noise-free case and the case with noise, even in the situation where both the additive noise and dilution noise exist. We also carry out simulations to compare the proposed algorithms and existing algorithms in the literature, the results of which reveal that the proposed algorithms require fewer tests and are robust in the presence of noise.