Bayesian Design for Random Walk Barriers

We study the optimal design of absorption barriers and sample size for a simple random walk. High barriers yield more informative experiments, but may be more costly. We obtain optimal designs that are balancing the relative advantages of choosing a high barrier with few replications versus a lower barrier with more replications. We address the problem from a Bayesian, decision theoretic, viewpoint, by using a utility function based on a limiting form of Shannon information. After discussing properties of the optimal designs, we apply the results to a model describing the growth of cancer cells, and we illustrate how the selection of the prior distribution influences the solution.