The use of Thompson sampling to increase estimation precision

In this article, we consider a sequential sampling scheme for efficient estimation of the difference between the means of two independent treatments when the population variances are unequal across groups. The sampling scheme proposed is based on a solution to bandit problems called Thompson sampling. While this approach is most often used to maximize the cumulative payoff over competing treatments, we show that the same method can also be used to balance exploration and exploitation when the aim of the experimenter is to efficiently increase estimation precision. We introduce this novel design optimization method and, by simulation, show its effectiveness.