A Laplace-based algorithm for Bayesian adaptive design
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A Laplace-based algorithm for Bayesian adaptive design S. G. J. Senarathne1 · C. C. Drovandi1 · J. M. McGree1 Received: 25 July 2019 / Accepted: 3 March 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract 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. Keywords Importance sampling · Model discrimination · Parameter estimation · Pareto smoothing · Sequential Monte Carlo · Total entropy
1 Introduction Bayesian adaptive design is an integral component of scientific investigation in fields such as the physical, chemical and biological sciences (Roy and Notz 2014; Barz et al. 2016; Antognini and Giovagnoli 2015). The approach is to, based on current prior information about the experimental outcomes, find a design to collect the next data point or batch of data. Once this design has been selected, data are collected, and the prior information for the experiment is updated to reflect the new information gained from the new data. This process then iterates a fixed number of times or until a certain stopping criterion has been met. At each iteration, the choice of design is determined by maximising an expected utility function over the space of all possible designs, where the expectation is with respect to the joint distribution of
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S. G. J. Senarathne [email protected]; [email protected] School of Mathematical Sciences, Science and Engineering Faculty, Queensland University of Technology, Brisbane, Australia
the candidate models, the parameters and the experimental outcomes. The expected utility is defined to e
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