Some Bayesian Experimental Design Theory for Risk Reduction in Extrapolation

Decision problems depending on extrapolation promise to become increasingly important. The key problem is determining if the model being used for extrapolation is going to give reasonable results, or err in a dangerous manner. Ideally, as one proceeds from investigation to decision, some guidance should be present based on the goal as to which investigation will reduce the risk the most given the cost. In this report, a very simple version of the problem is formalized and examined. The result is, interestingly, that the best evidence in support of the favored model is a null result in the experiment most likely to raise doubt over that model. The theory is applied to a simple example drawn from accelerated testing.