Bayesian Optimal Designs for Experiments on Networks

Music City Center 

We consider the problem of designing an experiment in which experimental units are connected on a network. To find optimal designs for such experiments, the experimental outcomes are assumed to follow a network-outcome model in which units potentially influence one another. Due to network interference, these outcome models are often complex, and design criteria derived based on such models involve unknown parameters, and thus cannot be directly evaluated without making assumptions about these parameters' values. We mitigate this problem by defining a Bayesian design criterion, which is the mean squared error of the average treatment effect estimator integrated over a prior distribution for the unknown parameters. In general, this criterion does not have a closed-form formula, and so traditional algorithms to solve for optimal designs cannot be applied. Instead, we propose and study the use of the genetic algorithm to find near-optimal designs. Through simulations with various real-life networks and network-outcome models, we demonstrate the robust performance of our method compared to existing design construction strategies.