Calculation of Bayesian posteriors and model evidences typically requires numerical integration. Bayesian quadrature (BQ), a surrogate-model-based approach to numerical integration, is capable of superb sample efficiency, but its lack of parallelisation has hindered its practical applications. In this work, we propose a parallelised (batch) BQ method, employing techniques from kernel quadrature, that possesses an empirically exponential convergence rate. Additionally, just as with Nested Sampling, our method permits simultaneous inference of both posteriors and model evidence. Samples from our BQ surrogate model are re-selected to give a sparse set of samples, via a kernel recombination algorithm, requiring negligible additional time to increase the batch size. Empirically, we find that our approach significantly outperforms the sampling efficiency of both state-of-the-art BQ techniques and Nested Sampling in various real-world datasets, including lithium-ion battery analytics.

翻译：贝叶斯后验分布和模型证据的计算通常需要数值积分。贝叶斯求积（BQ）作为一种基于代理模型的数值积分方法，具有出色的样本效率，但其缺乏并行化能力限制了实际应用。本文提出一种并行化（批量）BQ方法，采用核求积技术，具有经验性的指数收敛速度。此外，与嵌套采样类似，该方法可同时推断后验分布和模型证据。通过核重组算法，从BQ代理模型中重新选择样本以获得稀疏样本集，而增加批量大小所需的额外时间可忽略不计。实验表明，在包括锂离子电池分析在内的多个真实数据集中，该方法在采样效率上显著优于最先进的BQ技术和嵌套采样。