Designing Real and Numerical Experiments with Uncertainties in Mind

We review principles for designing real and numerical experiments with uncertainties in mind, emphasizing the role of Bayesian Experimental Design in guiding data collection under uncertainty. After outlining key concepts relevant to both physical experiments (i.e., real-world experiments) and computationally intensive numerical experiments (i.e., computer simulations), we focus on sequential design strategies—commonly referred to as active learning in machine learning—that aim to maximize information gain in numerical experiments. When the goal is parameter inference, we propose a principled framework that balances exploration of the parameter space with the cost of acquiring new data. The approach leverages posterior-driven acquisition functions and is applicable to both deterministic and stochastic computer experiments. Finally, we introduce an open-source software package that enables adaptive experiment design across diverse applications, helping users prioritize experiments that yield the greatest inferential improvement given limited resources.