Risk-aware experimental design improves prediction for rare outcomes
Risk-Aware Goal-Oriented Bayesian Optimal Experimental Design
Computational Engineering, Finance, and Science
Summary
Traditional methods pick measurements to better understand model details but don’t always help with important predictions. The authors propose a new approach that focuses on measurements that improve predictions, especially for rare but high-risk events. Their method lets users specify what kinds of risks matter most and uses math techniques to efficiently find the best measurement plans. They tested this on a problem involving sensor placement for tracking how substances spread and showed it works better than standard methods.
What this means in practice
- •For environmental monitoring teams: Choose sensor locations that better detect rare but critical pollutant spreads using risk-focused experimental designs.
- •For industrial process control engineers: Improve measurement setups that prioritize prediction accuracy for unexpected failures or events by applying risk-aware experimental design.
Authors
John D. Jakeman, Rebekah White, Bart van Bloemen Waanders, Drew P. Kouri, Alen Alexanderian
Abstract
Traditional Bayesian optimal experimental design (OED) selects measurements that best inform a model's parameters. However, such measurements can be suboptimal for downstream predictions. Goal-oriented OED targets the prediction directly. However, the existing goal-oriented criteria value all reductions in predictive uncertainty equally, with no way to prioritize rare, high-consequence outcomes. In this article, we develop a risk-aware framework that composes risk at three levels, each generalizing an ingredient of classical $I$- and $G$-optimal design: a deviation measure of the posterior predictive uncertainty (generalizing the predictive variance), a risk measure across the prediction domain (interpolating $I$-optimal averaging and $G$-optimal worst-case selection), and a risk measure over datasets (generalizing the expectation). We generate each level from a regret function in the risk quadrangle, so that one triple specifies a practitioner's risk preference. We relax the design to continuous weights on the unit simplex and construct a nested-quadrature estimator that is differentiable in the design variable. This enables solving the optimal design problem with gradient-based methods, avoiding a combinatorial search over candidate designs. For a linear-Gaussian lognormal model and a nonlinear extension, we derive closed-form objectives. These give exact references against which we verify that the estimator converges. We demonstrate this framework for finding optimal sensor placements in an inverse problem governed by an advection-diffusion equation. We find that the risk-aware designs substantially outperform the expected-information-gain baseline, which is statistically indistinguishable from a random allocation.