Mathematical Conversations

Discrepancy theory tells us that it is possible to partition vectors into sets so that each set looks surprisingly similar to every other. By "surprisingly similar" we mean much more similar than a random partition. Randomized Controlled Trials are used to test the effectiveness of interventions, like medical treatments. Randomization is used to ensure that the test and control groups are probably similar. When we know nothing about the experimental subjects, uniform random assignment is the best we can do. When we have information about the experimental subjects that is likely to be correlated with medical outcomes, we can try to combine the strengths of randomization with the promises of discrepancy theory. This should allow us to obtain more accurate estimates of the effectiveness of treatments, or to conduct trials with fewer experimental subjects. This intersection raises many exciting problems in discrepancy theory and experimental design.

On Monday, May 11, I will present a paper on this topic that Christopher Harshaw, Fredrik Sävje, and Peng Zhang and I are finishing writing.