# Bayesian design of experiments for intractable likelihood models using coupled auxiliary models and multivariate emulation

arXiv: https://arxiv.org/abs/1803.07018 · HTML: https://mlsanity.com/paper/1803.07018/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Mar 2018.

## Built on by (most cited first, 10 of 10)

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- [Implicit Deep Adaptive Design: Policy-Based Experimental Design without Likelihoods](https://mlsanity.com/paper/2111.02329/) (2021)
- [Gradient-based Bayesian Experimental Design for Implicit Models using Mutual Information Lower Bounds](https://mlsanity.com/paper/2105.04379/) (2021)
- [Step-DAD: Semi-Amortized Policy-Based Bayesian Experimental Design](https://mlsanity.com/paper/2507.14057/) (2025)
- [A Scalable Gradient-Free Method for Bayesian Experimental Design with Implicit Models](https://mlsanity.com/paper/2103.08026/) (2021)
- [Bayesian Optimal Experimental Design for Simulator Models of Cognition](https://mlsanity.com/paper/2110.15632/) (2021)
- [A Likelihood-Free Approach to Goal-Oriented Bayesian Optimal Experimental Design](https://mlsanity.com/paper/2408.09582/) (2024)
- [Efficient Discretizations of Optimal Transport](https://mlsanity.com/paper/2102.07956/) (2021)
- [A Hybrid Gradient Method to Designing Bayesian Experiments for Implicit Models](https://mlsanity.com/paper/2103.08594/) (2021)

## Abstract (arXiv)

A Bayesian design is given by maximising an expected utility over a design space. The utility is chosen to represent the aim of the experiment and its expectation is taken with respect to all unknowns: responses, parameters and/or models. Although straightforward in principle, there are several challenges to finding Bayesian designs in practice. Firstly, the utility and expected utility are rarely available in closed form and require approximation. Secondly, the design space can be of high-dimensionality. In the case of intractable likelihood models, these problems are compounded by the fact that the likelihood function, whose evaluation is required to approximate the expected utility, is not available in closed form. A strategy is proposed to find Bayesian designs for intractable likelihood models. It relies on the development of an automatic, auxiliary modelling approach, using multivariate Gaussian process emulators, to approximate the likelihood function. This is then combined with a copula-based approach to approximate the marginal likelihood (a quantity commonly required to evaluate many utility functions). These approximations are demonstrated on examples of stochastic process models involving experimental aims of both parameter estimation and model comparison.