Bayesian optimal design for changepoint problems

Abstract

We investigate Bayesian optimal designs for changepoint problems. We find robust optimal designs which allow for arbitrary distributions before and after the change, arbitrary prior densities on the parameters before and after the change, and any log‐concave prior density on the changepoint. We define a new design measure for Bayesian optimal design problems as a means of finding the optimal design. Our results apply to any design criterion function concave in the design measure. We illustrate our results by finding the optimal design in a problem motivated by a previous clinical trial. The Canadian Journal of Statistics 37: 495–513; 2009 © 2009 Statistical Society of Canada

A D-Optimal Design for Estimation of Parameters of an Exponential-Linear Growth Curve of Nanostructures

“…As explained earlier, this is not the case in our experimental setting, which can be considered "off-line" in the sense that an experimental unit can generate only a single data point at the time. Consequently, the assumptions used in Atherton et al (2009) (prespecified distance d between any two design points and no replicated observation) do not hold in the current problem. There has also been some recent work on D-optimal designs for spline models (Biedermann, Dette, and Woods 2011).…”

“…However, our problem does not have the typical "online" nature associated with the problem considered by Atherton et al (2009) and most change-point problems. Typically, in such problems the experimenter continues to observe the process over time and has to decide when a change has occurred in the generative parameters of the data sequence.…”

“…There has been some recent work on Bayesian D-optimal design with change points (Atherton et al 2009). However, our problem does not have the typical "online" nature associated with the problem considered by Atherton et al (2009) and most change-point problems.…”

Sample size and classification error for Bayesian change-point models with unlabelled sub-groups and incomplete follow-up

“…Bischoff and Miller 25 derived frequentist optimal designs to detect the existence of a change-point in the single-path setting. Atherton et al., 26 also for the single-path setting but in the Bayesian framework, investigated the optimal location for observation times. There has been little work on optimal design for the so-called multi-path change-point problem, which is the setting of our paper, with repeated observations on multiple individuals.…”