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

机译：一种基于损失函数的基于正态近似的完全贝叶斯最优设计的方法

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摘要

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.
机译：决策理论贝叶斯最优设计的生成由于在潜在的高维设计空间上最小化分析上难以处理的预期损失函数的重大计算挑战而变得复杂。提出了一种新的近似寻找贝叶斯最优设计的通用方法，该方法使用计算效率高的基于法线的近似对后验求和，以帮助近似预期损失。在说明性但具有挑战性的示例中演示了这种新方法，这些示例包括用于分块实验的分层模型以及参数估计和模型区分的实验目标。在可能的情况下，将所建议方法的结果在性能和计算时间上与使用计算上更昂贵但可能更准确的蒙特卡洛近似所得到的结果进行比较。此外，该方法还适用于在计算上无法使用蒙特卡罗近似的问题。

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