We present a flexible method for computing Bayesian optimal experimental designs (BOEDs) for inverse problems with intractable posteriors. The approach is applicable to a wide range of BOED problems and can accommodate various optimality criteria, prior distributions and noise models. The key to our approach is the construction of a transport-map-based surrogate to the joint probability law of the design, observational and inference random variables. This order-preserving transport map is constructed using tensor trains and can be used to efficiently sample from (and evaluate approximate densities of) conditional distributions that are used to define many commonly-used optimality criteria. The algorithm is also extended to sequential data acquisition problems, where experiments can be performed in sequence and used to update the state of knowledge about the unknown parameters. The sequential BOED problem is made computationally feasible by preconditioning the approximation of the joint density at the current stage using transport maps constructed at previous stages. The flexibility of our approach in finding optimal designs is illustrated with some numerical examples inspired by disease modeling and the reconstruction of subsurface structures in aquifers.

翻译：我们提出了一种灵活的方法，用于计算具有难处理后验的反问题的贝叶斯最优实验设计（BOED）。该方法适用于广泛的BOED问题，并能适应多种最优性准则、先验分布和噪声模型。该方法的核心是构建基于传输映射的代理模型，以逼近设计变量、观测变量和推理变量的联合概率分布。这种保序传输映射利用张量列构建，可用于高效地从条件分布中采样（并评估其近似密度），这些条件分布常用于定义众多常见的最优性准则。该算法还扩展至序贯数据采集问题，其中实验可依次进行，并用于更新关于未知参数的知识状态。通过利用先前阶段构建的传输映射对当前阶段的联合密度近似进行预处理，使序贯BOED问题在计算上变得可行。我们通过受疾病建模和含水层地下结构重建启发的数值示例，展示了该方法在寻找最优设计方面的灵活性。