Bayesian Experimental Design

Bayesian experimental design studies how to choose experiments or measurements sequentially when observations are costly and uncertainty matters. Common approaches select designs by expected information gain or posterior uncertainty, often using Gaussian processes, Monte Carlo estimates, or amortized neural policies; Bayesian optimization and active learning extend these ideas to expensive black-box problems. Applications range from scientific parameter estimation and sensor placement to clinical questioning, reliability testing, and adaptive data collection. A central tension is that the most informative experiment may not improve a downstream decision, while model error, constraints, and computational cost can make standard information-gain criteria unreliable or impractical.