A Nonmathematical Review of Optimal Operator and Experimental Design for Uncertain Scientific Models with Application to Genomics.

Introduction: The most basic aspect of modern engineering is the design of operators to act on physical systems in an optimal manner relative to a desired objective - for instance, designing a con-trol policy to autonomously direct a system or designing a classifier to make decisions regarding the sys-tem. These kinds of problems appear in biomedical science, where physical models are created with the intention of using them to design tools for diagnosis, prognosis, and therapy.

Methods: In the classical paradigm, our knowledge regarding the model is certain; however, in practice, especially with complex systems, our knowledge is uncertain and operators must be designed while tak-ing this uncertainty into account. The related concepts of intrinsically Bayesian robust operators and op-timal Bayesian operators treat operator design under uncertainty. An objective-based experimental de-sign procedure is naturally related to operator design: We would like to perform an experiment that max-imally reduces our uncertainty as it pertains to our objective.

Results & Discussion: This paper provides a nonmathematical review of optimal Bayesian operators directed at biomedical scientists. It considers two applications important to genomics, structural interven-tion in gene regulatory networks and classification.

Conclusion: The salient point regarding intrinsically Bayesian operators is that uncertainty is quantified relative to the scientific model, and the prior distribution is on the parameters of this model. Optimization has direct physical (biological) meaning. This is opposed to the common method of placing prior distri-butions on the parameters of the operator, in which case there is a scientific gap between operator design and the phenomena.