# Bayesian Experimental Design for Implicit Models by Mutual Information Neural Estimation

arXiv: https://arxiv.org/abs/2002.08129 · HTML: https://mlsanity.com/paper/2002.08129/

## Key facts

- Cited by 56 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Feb 2020.

## Built on by (most cited first, 30 of 56)

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- [Optimizing Sequential Experimental Design with Deep Reinforcement Learning](https://mlsanity.com/paper/2202.00821/) (2022)
- [Gradient-based Bayesian Experimental Design for Implicit Models using Mutual Information Lower Bounds](https://mlsanity.com/paper/2105.04379/) (2021)
- [BED-LLM: Intelligent Information Gathering with LLMs and Bayesian Experimental Design](https://mlsanity.com/paper/2508.21184/) (2025)
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- [Batch Multi-Fidelity Active Learning with Budget Constraints](https://mlsanity.com/paper/2210.12704/) (2022)
- [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)
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- [Variational Bayesian Optimal Experimental Design with Normalizing Flows](https://mlsanity.com/paper/2404.13056/) (2024)
- [Robust Expected Information Gain for Optimal Bayesian Experimental Design Using Ambiguity Sets](https://mlsanity.com/paper/2205.09914/) (2022)
- [Step-DAD: Semi-Amortized Policy-Based Bayesian Experimental Design](https://mlsanity.com/paper/2507.14057/) (2025)
- [Goal-Oriented Bayesian Optimal Experimental Design for Nonlinear Models using Markov Chain Monte Carlo](https://mlsanity.com/paper/2403.18072/) (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)
- [Deep Bayesian Active Learning for Accelerating Stochastic Simulation](https://mlsanity.com/paper/2106.02770/) (2021)
- [Statistically Efficient Bayesian Sequential Experiment Design via Reinforcement Learning with Cross-Entropy Estimators](https://mlsanity.com/paper/2305.18435/) (2023)
- [Statistical applications of contrastive learning](https://mlsanity.com/paper/2204.13999/) (2022)
- [On Estimating the Gradient of the Expected Information Gain in Bayesian Experimental Design](https://mlsanity.com/paper/2308.09888/) (2023)
- [PASOA- PArticle baSed Bayesian Optimal Adaptive design](https://mlsanity.com/paper/2402.07160/) (2024)
- [Bayesian Optimal Experimental Design for Simulator Models of Cognition](https://mlsanity.com/paper/2110.15632/) (2021)
- [Bayesian Active Learning for Discrete Latent Variable Models](https://mlsanity.com/paper/2202.13426/) (2022)
- [When Bioprocess Engineering Meets Machine Learning: A Survey from the Perspective of Automated Bioprocess Development](https://mlsanity.com/paper/2209.01083/) (2022)
- [CO-BED: Information-Theoretic Contextual Optimization via Bayesian Experimental Design](https://mlsanity.com/paper/2302.14015/) (2023)
- [JADAI: Jointly Amortizing Adaptive Design and Bayesian Inference](https://mlsanity.com/paper/2512.22999/) (2025)
- [Efficient Real-world Testing of Causal Decision Making via Bayesian Experimental Design for Contextual Optimisation](https://mlsanity.com/paper/2207.05250/) (2022)
- [Online simulator-based experimental design for cognitive model selection](https://mlsanity.com/paper/2303.02227/) (2023)

## Abstract (arXiv)

Implicit stochastic models, where the data-generation distribution is intractable but sampling is possible, are ubiquitous in the natural sciences. The models typically have free parameters that need to be inferred from data collected in scientific experiments. A fundamental question is how to design the experiments so that the collected data are most useful. The field of Bayesian experimental design advocates that, ideally, we should choose designs that maximise the mutual information (MI) between the data and the parameters. For implicit models, however, this approach is severely hampered by the high computational cost of computing posteriors and maximising MI, in particular when we have more than a handful of design variables to optimise. In this paper, we propose a new approach to Bayesian experimental design for implicit models that leverages recent advances in neural MI estimation to deal with these issues. We show that training a neural network to maximise a lower bound on MI allows us to jointly determine the optimal design and the posterior. Simulation studies illustrate that this gracefully extends Bayesian experimental design for implicit models to higher design dimensions.