Do sequential tests help in group testing?

Dr Matthew Aldridge, University of Leeds. Part of Probability, Stochastic Modelling and Financial Mathematics seminar.

Suppose you wish to use a blood test to screen a group of people for a rare disease. You could take a blood sample from each person and test the samples individually. However, it can be more efficient to mix a number of samples together and test that mixture: if the test comes back negative then none of those people have the disease, while if the test is positive then at least one of them has the disease and further investigation is needed. 

This problem is called group testing: given n people of whom k have the disease, how many of these mixed tests do we need to find out which people are infected? Tests could be performed sequentially, where the result of each test is seen before designing the next test, but it's often more convenient to perform them nonsequentially, so all tests can be performed at once in parallel.

We'll see that sometimes performing tests sequentially can improve performance but that sometimes there's no advantage.

Dr Matthew Aldridge, University of Leeds.