Bayesian experimental design

Bayesian experimental design is a general probability-theoretical framework from which other theories of experimental design can be derived. It uses Bayesian inference to interpret the observations gathered during an experiment, which lets the designer account both for prior knowledge about the parameters to be determined and for uncertainty in the observations. The theory rests partly on the theory of making optimal decisions under uncertainty. The aim in designing an experiment is to maximize the expected utility of its outcome. That utility is most often defined as a measure of how accurate the information from the experiment is, for example the Shannon information or the negative of the variance, but it can also include factors such as the financial cost of running the experiment. Which design is optimal therefore depends on the utility criterion chosen. When the model is linear, the prior is homogeneous and the observational errors are normally distributed, the theory simplifies to classical optimal experimental design.