# Bayesian optimal experimental design with Wasserstein information criteria

arXiv: https://arxiv.org/abs/2504.10092 · HTML: https://mlsanity.com/paper/2504.10092/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Apr 2025.

## Built on by (most cited first, 8 of 8)

- [A Geometric Approach to Optimal Experimental Design](https://mlsanity.com/paper/2510.14848/) (2025)
- [Bayesian Experimental Design for Model Discrepancy Calibration: An Auto-Differentiable Ensemble Kalman Inversion Approach](https://mlsanity.com/paper/2504.20319/) (2025)
- [Approximation of differential entropy in Bayesian optimal experimental design](https://mlsanity.com/paper/2510.00734/) (2025)
- [Bayesian Experimental Design for Model Discrepancy Calibration: A Rivalry between Kullback--Leibler Divergence and Wasserstein Distance](https://mlsanity.com/paper/2601.16425/) (2026)
- [Beyond Expected Information Gain: Stable Bayesian Optimal Experimental Design with Integral Probability Metrics and Plug-and-Play Extensions](https://mlsanity.com/paper/2604.21849/) (2026)
- [Active Learning for Communication Structure Optimization in LLM-Based Multi-Agent Systems](https://mlsanity.com/paper/2605.05703/) (2026)
- [A Convex Approximation Framework for Neural Likelihood-Based Bayesian Inverse Problems](https://mlsanity.com/paper/2607.06252/) (2026)
- [Uncertainty quantification in mechanics: A unified Bayesian perspective](https://mlsanity.com/paper/2607.18734/) (2026)

## Abstract (arXiv)

Bayesian optimal experimental design (OED) provides a principled framework for selecting observations or experiments. We introduce new Bayesian design criteria based on the expected Wasserstein-p distance between the prior and posterior distributions, termed Wasserstein information criteria. These criteria have many parallels with the widely used expected information gain (EIG) criterion, which instead relies on the Kullback--Leibler divergence. We show that the Wasserstein-2 criterion admits a closed-form solution in the linear-Gaussian setting, a property which can be used for more general approximation schemes, and contrast this solution with classical notions of Bayesian alphabetic optimality. Then we develop a stability analysis of the Wasserstein-1 criterion, wherein we bound errors induced by perturbations of the prior or likelihood. We partially extend this analysis to the Wasserstein-2 criterion. In particular, these results yield error rates for empirical approximations of the prior. We then illustrate the computability of the Wasserstein-2 criterion and demonstrate our approximation rates through simulations.