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（亦称为边际似然）的方法，该证据表示似然函数在先验分布上的积分。更广义而言，它是一种数值概率求积规则。嵌套抽样的核心思想是通过合适的变换将参数空间上的高维似然积分转化为单位区间上的积分。具体实现时，一组活跃样本沿被积函数的水平集逐级上升，并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存在非平凡平台的被积函数的有效性，并展示了嵌套抽样在估计稀有事件（对数）概率时的实际效能。