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

TL;DR

This paper introduces a Bayesian experimental design method for intractable likelihood models, using auxiliary models and multivariate emulation to approximate likelihoods and utilities, enabling efficient design in complex stochastic process models.

Contribution

It develops an automatic auxiliary modeling approach with Gaussian process emulators and copula-based methods to facilitate Bayesian design for intractable likelihood models.

Findings

Effective approximation of likelihood functions in complex models.

Successful application to stochastic process models for parameter estimation.

Demonstrated improvements in design efficiency and utility evaluation.

Abstract

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.