arXiv subjects

Rebekah White

Publications and source records attributed to Rebekah White.

4 recordsLinked to original sources

arXiv2026

Risk-Aware Goal-Oriented Bayesian Optimal Experimental Design

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.

stat.ME↗

arXiv2026

Duality and Error for Predictively Oriented Inference

Predictively oriented (PrO) inference quantifies uncertainty by selecting a distribution over model parameters to optimize a scoring rule applied to the induced predictive distribution, together with a divergence penalty from a reference distribution. By applying the scoring rule after averaging model densities, PrO inference targets predictive performance, accounting for model misspecification. We focus on the logarithmic score with general $\phi$-divergence regularization. Our contributions are twofold. First, we derive a finite-dimensional dual formulation of PrO inference. For $n$ observations, the dual problem has $n+1$ variables. We establish zero-duality-gap criteria and optimality conditions that relate the primal and dual solutions. When primal and dual solutions exist, these conditions yield a semi-analytical representation of the PrO posterior and certificates for assessing the accuracy of numerical solutions. For Kullback--Leibler regularization, the posterior has an exponential form. Second, we derive a finite-sample excess predictive-risk bound for approximate PrO posteriors that separates sampling fluctuation, approximation under a divergence budget, regularization, and numerical optimization error. The result applies even when the benchmark predictive risk is not attained by any probability distribution over the model parameters having finite divergence from the reference distribution. We use an exactly solvable categorical example to show that predictive-risk convergence can imply convergence to a unique predictive distribution even though the parameter distributions have no weak limit on the original parameter space. The example also shows that different $\phi$-divergences can require different regularization schedules. We conclude with a misspecified Gaussian location-mixture example that illustrates the dual computation, primal recovery, and numerical accuracy checks.

stat.ME↗

arXiv2026

Robust Optimal Experimental Design Accounting for Sensor Failure

Optimal experimental design provides a way of determining a-priori the best locations at which to place accelerometers in vibrations analysis experiments. However, in practice, sensors often fail during experimentation due high mechanical accelerations. There have been limited works exploring the use of robust OED in the context of vibrations analysis, where design spaces (i.e. candidate sensor locations and orientations) are high-dimensional and the finite-element models are expensive to compute. Therefore, this work considers the application of more general robust OED formulations to such a structural dynamics problem. We employ a relaxation-based approach that enables the use of efficient gradient-based optimization. Furthermore, we leverage a binary-inducing penalty during optimization to provide a binary sensor design as an alternative to leveraging post-optimization rounding heuristics. We consider performance metrics based on the log-determinant of the parameter covariance as well those based on parameter and prediction mean-squared errors. We find that although robust and classical designs are similar for the structural dynamics problem of interest, robust designs outperform classical designs on average over relevant failure scenarios of interest.

cs.CE↗

arXiv2026

Inference in the presence of model-form uncertainties: Leveraging a prediction-oriented approach to improve uncertainty characterization

Bayesian inference is a popular approach to calibrating uncertainties, but it can underpredict such uncertainties when model misspecification is present, impacting its reliability to inform decision making. Recently, the statistics and machine learning communities have developed prediction-oriented inference approaches that provide better calibrated uncertainties and adapt to the level of misspecification present. However, these approaches have yet to be demonstrated in the context of complex scientific applications where phenomena of interest are governed by physics-based models. Such settings often involve single realizations of high-dimensional spatio-temporal data and nonlinear, computationally expensive parameter-to-observable maps. This work investigates variational prediction-oriented inference in problems exhibiting these relevant features; namely, we consider a polynomial model and a contaminant transport problem governed by advection-diffusion equations. The prediction-oriented loss is formulated as the log-predictive probability of the calibration data. We study the effects of increasing misspecification and noise, and we assess approximations of the predictive density using Monte Carlo sampling and component-wise kernel density estimation. A novel aspect of this work is applying prediction-oriented inference to the calibration of model-form uncertainty (MFU) representations, which are embedded physics-based modifications to the governing equations that aim to reduce (but rarely eliminate) model misspecification. The computational results demonstrate that prediction-oriented frameworks can provide better uncertainty characterizations in comparison to standard inference while also being amenable to the calibration of MFU representations.

cs.CE↗