We introduce a novel technique within the Nested Sampling framework to enhance efficiency of the computation of Bayesian evidence, a critical component in scientific data analysis. In higher dimensions, Nested Sampling relies on Markov Chain-based likelihood-constrained prior samplers, which generate numerous 'phantom points' during parameter space exploration. These points are too auto-correlated to be used in the standard Nested Sampling scheme and so are conventionally discarded, leading to waste. Our approach discovers a way to integrate these phantom points into the evidence calculation, thereby improving the efficiency of Nested Sampling without sacrificing accuracy. This is achieved by ensuring the points within the live set remain asymptotically i.i.d. uniformly distributed, allowing these points to contribute meaningfully to the final evidence estimation. We apply our method on several models, demonstrating substantial enhancements in sampling efficiency, that scales well in high-dimension. Our findings suggest that this approach can reduce the number of required likelihood evaluations by at least a factor of 5. This advancement holds considerable promise for improving the robustness and speed of statistical analyses over a wide range of fields, from astrophysics and cosmology to climate modelling.

翻译：我们在嵌套抽样框架中引入了一项新技术，旨在提升贝叶斯证据计算的效率——这是科学数据分析中的关键组成部分。在高维情形下，嵌套抽样依赖于基于马尔可夫链的似然约束先验采样器，其在参数空间探索过程中会产生大量“幻影点”。由于这些点自相关性过强，无法用于标准嵌套抽样方案，因此通常被丢弃，造成浪费。我们的方法发现了一种将这些幻影点整合到证据计算中的途径，从而在保持精度的前提下提升嵌套抽样的效率。这是通过确保存活集合内的点保持渐近独立同分布均匀分布来实现的，使得这些点能够对最终证据估计做出有意义的贡献。我们将该方法应用于多个模型，展示了采样效率的显著提升，且该性能在高维情况下具有良好的扩展性。研究结果表明，该方法至少可将所需似然评估次数减少5倍。这一进展有望显著提升从天体物理学与宇宙学到气候建模等广泛领域内统计分析的稳健性与速度。