AI 中文总结
该研究针对嵌套采样效率受限问题，在BEST中实现了基于TensorFlow的高效嵌套采样方法，通过批量活点更新等技术提升速度，经测试可准确计算贝叶斯证据，适用于向量化似然与模拟器推断。
AI 中文摘要
嵌套采样被广泛用于贝叶斯证据计算，但其固有的顺序结构限制了对现代向量化似然和模拟器的利用效率。我们提出了一种全新的嵌套采样实现，完全基于TensorFlow编写，命名为\textsc{best}，专为在CPU和GPU上进行高效XLA编译而设计。该采样器将聚类与切片采样相结合，支持同时更新多个活点。由于批量处理打破了传统嵌套采样的严格顺序，我们引入了排序和基于历史的校正方法，以降低由此产生的证据估计偏差。我们在高斯、Rosenbrock和多模态似然上对该采样器进行了测试，并将其性能与JAXNS和UltraNest进行了比较。结果表明，对于中等批量大小，可保留准确的证据估计，其中$m/N_{\rm live}\lesssim 0.1$提供了实用的有效范围。最后，利用27维宇宙学似然模拟器，我们证明批量活点更新可大幅减少挂钟时间，同时在报告的不确定度范围内与顺序采样保持一致。因此，该新实现为\textsc{best}扩展了一种高效的嵌套采样方法，适用于快速、向量化似然及基于模拟器的推断。
英文摘要
Nested sampling is widely used for Bayesian evidence computation, but its intrinsically sequential structure limits how efficiently it can exploit modern vectorised likelihoods and emulators. We present a new nested-sampling implementation in \textsc{best}, written entirely in TensorFlow and designed for efficient XLA compilation on both CPUs and GPUs. The sampler combines clustering and slice sampling with the possibility of updating several live points simultaneously. Since batching breaks the strict ordering of conventional nested sampling, we introduce sorting and history-based corrections to reduce the resulting bias in the evidence estimate. We test the sampler on Gaussian, Rosenbrock, and multimodal likelihoods and compare its performance with JAXNS and UltraNest. The results show that accurate evidence estimates can be retained for moderate batch sizes, with $m/N_{\rm live}\lesssim 0.1$ providing a useful practical regime. Finally, using a 27-dimensional cosmological likelihood emulator, we show that batched live-point updates can substantially reduce the wall-clock time while remaining consistent with sequential sampling within the reported uncertainties. The new implementation therefore extends \textsc{best} with an efficient nested-sampling method tailored to fast, vectorised likelihoods and emulator-based inference.
Comments22 pages, 6 figures, 2 tables
