# Goal-Oriented Bayesian Optimal Experimental Design for Nonlinear Models using Markov Chain Monte Carlo

arXiv: https://arxiv.org/abs/2403.18072 · HTML: https://mlsanity.com/paper/2403.18072/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 58 references that are in the map.
- First posted on arXiv 26 Mar 2024.

## Builds on (most cited first, 11 of 11)

- [A Tutorial on Bayesian Optimization](https://mlsanity.com/paper/1807.02811/) (2018)
- [On Variational Bounds of Mutual Information](https://mlsanity.com/paper/1905.06922/) (2019)
- [Modern Bayesian Experimental Design](https://mlsanity.com/paper/2302.14545/) (2023)
- [Variational Bayesian Optimal Experimental Design](https://mlsanity.com/paper/1903.05480/) (2019)
- [Recent Advances in Bayesian Optimization](https://mlsanity.com/paper/2206.03301/) (2022)
- [Bayesian Experimental Design for Implicit Models by Mutual Information Neural Estimation](https://mlsanity.com/paper/2002.08129/) (2020)
- [Goal-Oriented Optimal Design of Experiments for Large-Scale Bayesian Linear Inverse Problems](https://mlsanity.com/paper/1802.06517/) (2018)
- [A layered multiple importance sampling scheme for focused optimal Bayesian experimental design](https://mlsanity.com/paper/1903.11187/) (2019)
- [An efficient method for goal-oriented linear Bayesian optimal experimental design: Application to optimal sensor placemen](https://mlsanity.com/paper/2102.06627/) (2021)
- [Error Bounds for Sequential Monte Carlo Samplers for Multimodal Distributions](https://mlsanity.com/paper/1509.08775/) (2015)
- [An approach for finding fully Bayesian optimal designs using normal-based approximations to loss functions](https://mlsanity.com/paper/1608.05815/) (2016)

## Built on by (most cited first, 9 of 9)

- [Amortized Bayesian Experimental Design for Decision-Making](https://mlsanity.com/paper/2411.02064/) (2024)
- [Variational Bayesian Optimal Experimental Design with Normalizing Flows](https://mlsanity.com/paper/2404.13056/) (2024)
- [Spend Less, Fit Better: Budget-Efficient Scaling Law Fitting via Active Experiment Selection](https://mlsanity.com/paper/2604.22753/) (2026)
- [A Likelihood-Free Approach to Goal-Oriented Bayesian Optimal Experimental Design](https://mlsanity.com/paper/2408.09582/) (2024)
- [Goal-Oriented Sequential Bayesian Experimental Design for Causal Learning](https://mlsanity.com/paper/2507.07359/) (2025)
- [Action-BED: Task-Driven Bayesian Experimental Design with Singly Intractable Objectives](https://mlsanity.com/paper/2606.23662/) (2026)
- [Goal-driven Bayesian Optimal Experimental Design for Robust Decision-Making Under Model Uncertainty](https://mlsanity.com/paper/2605.26093/) (2026)
- [ShaplEIG: Bayesian Experimental Design for Shapley Value Estimation](https://mlsanity.com/paper/2606.02247/) (2026)
- [Information-theoretic receding-horizon active learning of nonlinear dynamical systems](https://mlsanity.com/paper/2609.36712/) (2026)

## Abstract (arXiv)

Optimal experimental design (OED) provides a systematic approach to quantify and maximize the value of experimental data. Under a Bayesian approach, conventional OED maximizes the expected information gain (EIG) on model parameters. However, we are often interested in not the parameters themselves, but predictive quantities of interest (QoIs) that depend on the parameters in a nonlinear manner. We present a computational framework of predictive goal-oriented OED (GO-OED) suitable for nonlinear observation and prediction models, which seeks the experimental design providing the greatest EIG on the QoIs. In particular, we propose a nested Monte Carlo estimator for the QoI EIG, featuring Markov chain Monte Carlo for posterior sampling and kernel density estimation for evaluating the posterior-predictive density and its Kullback-Leibler divergence from the prior-predictive. The GO-OED design is then found by maximizing the EIG over the design space using Bayesian optimization. We demonstrate the effectiveness of the overall nonlinear GO-OED method, and illustrate its differences versus conventional non-GO-OED, through various test problems and an application of sensor placement for source inversion in a convection-diffusion field.