# Sequential Bayesian Experimental Design for Implicit Models via Mutual Information

arXiv: https://arxiv.org/abs/2003.09379 · HTML: https://mlsanity.com/paper/2003.09379/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Mar 2020.

## Built on by (most cited first, 23 of 23)

- [Deep Adaptive Design: Amortizing Sequential Bayesian Experimental Design](https://mlsanity.com/paper/2103.02438/) (2021)
- [Implicit Deep Adaptive Design: Policy-Based Experimental Design without Likelihoods](https://mlsanity.com/paper/2111.02329/) (2021)
- [Optimizing Sequential Experimental Design with Deep Reinforcement Learning](https://mlsanity.com/paper/2202.00821/) (2022)
- [Bayesian Algorithm Execution: Estimating Computable Properties of Black-box Functions Using Mutual Information](https://mlsanity.com/paper/2104.09460/) (2021)
- [Gradient-based Bayesian Experimental Design for Implicit Models using Mutual Information Lower Bounds](https://mlsanity.com/paper/2105.04379/) (2021)
- [Bayesian Sequential Optimal Experimental Design for Nonlinear Models Using Policy Gradient Reinforcement Learning](https://mlsanity.com/paper/2110.15335/) (2021)
- [Tight Mutual Information Estimation With Contrastive Fenchel-Legendre Optimization](https://mlsanity.com/paper/2107.01131/) (2021)
- [Policy-Based Bayesian Experimental Design for Non-Differentiable Implicit Models](https://mlsanity.com/paper/2203.04272/) (2022)
- [Step-DAD: Semi-Amortized Policy-Based Bayesian Experimental Design](https://mlsanity.com/paper/2507.14057/) (2025)
- [Bayesian Experimental Design via Contrastive Diffusions](https://mlsanity.com/paper/2410.11826/) (2024)
- [Variational Sequential Optimal Experimental Design using Reinforcement Learning](https://mlsanity.com/paper/2306.10430/) (2023)
- [A Scalable Gradient-Free Method for Bayesian Experimental Design with Implicit Models](https://mlsanity.com/paper/2103.08026/) (2021)
- [Statistical applications of contrastive learning](https://mlsanity.com/paper/2204.13999/) (2022)
- [PASOA- PArticle baSed Bayesian Optimal Adaptive design](https://mlsanity.com/paper/2402.07160/) (2024)
- [Active Learning of Model Discrepancy with Bayesian Experimental Design](https://mlsanity.com/paper/2502.05372/) (2025)
- [Bayesian Optimal Experimental Design for Simulator Models of Cognition](https://mlsanity.com/paper/2110.15632/) (2021)
- [Designing Optimal Behavioral Experiments Using Machine Learning](https://mlsanity.com/paper/2305.07721/) (2023)
- [Constrained Bayesian Experimental Design via Online Planning](https://mlsanity.com/paper/2605.26990/) (2026)
- [MINIMALIST: Mutual INformatIon Maximization for Amortized Likelihood Inference from Sampled Trajectories](https://mlsanity.com/paper/2106.01808/) (2021)
- [A Hybrid Gradient Method to Designing Bayesian Experiments for Implicit Models](https://mlsanity.com/paper/2103.08594/) (2021)
- [Sequential Bayesian experimental designs via reinforcement learning](https://mlsanity.com/paper/2202.07472/) (2022)
- [ASBI: Leveraging Informative Real-World Data for Active Black-Box Simulator Tuning](https://mlsanity.com/paper/2510.15331/) (2025)
- [FairBED: A Bayesian Experimental Design Approach to Gathering Fairer Data](https://mlsanity.com/paper/2606.23515/) (2026)

## Abstract (arXiv)

Bayesian experimental design (BED) is a framework that uses statistical models and decision making under uncertainty to optimise the cost and performance of a scientific experiment. Sequential BED, as opposed to static BED, considers the scenario where we can sequentially update our beliefs about the model parameters through data gathered in the experiment. A class of models of particular interest for the natural and medical sciences are implicit models, where the data generating distribution is intractable, but sampling from it is possible. Even though there has been a lot of work on static BED for implicit models in the past few years, the notoriously difficult problem of sequential BED for implicit models has barely been touched upon. We address this gap in the literature by devising a novel sequential design framework for parameter estimation that uses the Mutual Information (MI) between model parameters and simulated data as a utility function to find optimal experimental designs, which has not been done before for implicit models. Our approach uses likelihood-free inference by ratio estimation to simultaneously estimate posterior distributions and the MI. During the sequential BED procedure we utilise Bayesian optimisation to help us optimise the MI utility. We find that our framework is efficient for the various implicit models tested, yielding accurate parameter estimates after only a few iterations.