Suppose that we have n people who have a disease, which can be discovered by blood test. It is possible to pool the blood samples of n people for a single test instead of testing each blood sample individually, and we test each person individually if the pooled blood sample's test is positive. Like this case, the method to pool together and analyze is called group testing. If the prevalence rate is small, group testing is better than individual test. Dorfman first suggested the idea, group testing for reducing the cost of detecting syphilis in U.S. soldiers.
In this thesis, we consider group testing for both cases where the prevalence rate(p) is known or unknown with no errors in test. For the case where the prevalence rate is unknown, we propose four heuristic methods which are very simple and easily implementable in the real world problems. On the uniform(0,1) prior distribution, the expected number of tests of the method-1 is larger than that of Sobel & Groll's method. However, the difference of expected number between the two methods is very small, and the method-1 has an advantage that it can be used easily in real problems. Moreover, the thesis is the first work, as far as the author understands, which deals with group testing problems under the setting of the beta prior distribution. For the case where the prevalence rate is known, we propose a generalized hierarchal dorfman procedure. In this procedure, we consider the edge effect and release the constraint that the subgroup's size should be equal.
