Bayesian Analysis

Bayesian Design of Experiments for Intractable Likelihood Models Using Coupled Auxiliary Models and Multivariate Emulation

Antony Overstall and James McGree

Full-text: Open access

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.

Article information

Source
Bayesian Anal., Volume 15, Number 1 (2020), 103-131.

Dates
First available in Project Euclid: 15 February 2019

Permanent link to this document
https://projecteuclid.org/euclid.ba/1550199643

Digital Object Identifier
doi:10.1214/19-BA1144

Mathematical Reviews number (MathSciNet)
MR4050879

Keywords
approximate Bayesian computation approximate coordinate exchange indirect inference Gaussian process model comparison parameter estimation

Rights
Creative Commons Attribution 4.0 International License.

Citation

Overstall, Antony; McGree, James. Bayesian Design of Experiments for Intractable Likelihood Models Using Coupled Auxiliary Models and Multivariate Emulation. Bayesian Anal. 15 (2020), no. 1, 103--131. doi:10.1214/19-BA1144. https://projecteuclid.org/euclid.ba/1550199643


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