An approach for finding fully Bayesian optimal designs using normal-based approximations to loss functions

TL;DR

This paper introduces a computationally efficient method for finding Bayesian optimal experimental designs using normal-based approximations to posterior summaries, reducing the need for costly Monte Carlo methods.

Contribution

A novel approach employing normal-based approximations to efficiently approximate expected loss in Bayesian optimal design problems, applicable to complex models.

Findings

The proposed method performs comparably to Monte Carlo approaches in accuracy.

It significantly reduces computational time for high-dimensional design spaces.

Applicable to problems where Monte Carlo methods are infeasible.

Abstract

The generation of decision-theoretic Bayesian optimal designs is complicated by the significant computational challenge of minimising an analytically intractable expected loss function over a, potentially, high-dimensional design space. A new general approach for approximately finding Bayesian optimal designs is proposed which uses computationally efficient normal-based approximations to posterior summaries to aid in approximating the expected loss. This new approach is demonstrated on illustrative, yet challenging, examples including hierarchical models for blocked experiments, and experimental aims of parameter estimation and model discrimination. Where possible, the results of the proposed methodology are compared, both in terms of performance and computing time, to results from using computationally more expensive, but potentially more accurate, Monte Carlo approximations. Moreover the methodology is also applied to problems where the use of Monte Carlo approximations is computationally infeasible.