A Laplace-based algorithm for Bayesian adaptive design

This article presents a novel Laplace-based algorithm that can be used to find Bayesian adaptive designs under model and parameter uncertainty. Our algorithm uses Laplace importance sampling to provide a computationally efficient approach to undertake adaptive design and inference when compared to standard approaches such as those based on the sequential Monte Carlo (SMC) algorithm. Like the SMC approach, our new algorithm requires very little problem-specific tuning and provides an efficient estimate of utility functions for parameter estimation and/or model choice. Further, within our algorithm, we adopt methods from Pareto smoothing to improve the robustness of the algorithm in forming particle approximations to posterior distributions. To evaluate our new adaptive design algorithm, three motivating examples from the literature are considered including examples where binary, multiple response and count data are observed under considerable model and parameter uncertainty. We benchmark the performance of our new algorithm against: (1) the standard SMC algorithm and (2) a standard implementation of the Laplace approximation in adaptive design. We assess the performance of each algorithm through comparing computational efficiency and design selection. The results show that our new algorithm is computationally efficient and selects designs that can perform as well as or better than the other two approaches. As such, we propose our Laplace-based algorithm as an efficient approach for designing adaptive experiments.