Nested Sampling is a method for computing the Bayesian evidence, also called the marginal likelihood, which is the integral of the likelihood with respect to the prior. More generally, it is a numerical probabilistic quadrature rule. The main idea of Nested Sampling is to replace a high-dimensional likelihood integral over parameter space with an integral over the unit line by employing a push-forward with respect to a suitable transformation. Practically, a set of active samples ascends the level sets of the integrand function, with the measure contraction of the super-level sets being statistically estimated. We justify the validity of this approach for integrands with non-negligible plateaus, and demonstrate Nested Sampling's practical effectiveness in estimating the (log-)probability of rare events.

翻译：嵌套抽样是一种计算贝叶斯证据（又称边际似然）的方法，其本质为似然函数对先验分布的积分。广义上，它属于一种数值概率求积规则。嵌套抽样的核心思想在于：通过利用适当的变换进行前向映射，将参数空间上的高维似然积分转化为单位线段上的积分。在实际操作中，一组活跃样本沿被积函数水平集逐级上升，同时通过统计方法估计超水平集的测度收缩。我们论证了该方法对具有不可忽略平台区间的被积函数的有效性，并展示了嵌套抽样在估计罕见事件（对数）概率方面的实际效能。