A number of distributions that arise in statistical applications can be expressed in the form of a weighted density: the product of a base density and a nonnegative weight function. Generating variates from such a distribution may be nontrivial and can involve an intractable normalizing constant. Rejection sampling may be used to generate exact draws, but requires formulation of a suitable proposal distribution. To be practically useful, the proposal must both be convenient to sample from and not reject candidate draws too frequently. A well-known approach to design a proposal involves decomposing the target density into a finite mixture, whose components may correspond to a partition of the support. This work considers such a construction that focuses on majorization of the weight function. This approach may be applicable when assumptions for adaptive rejection sampling and related algorithms are not met. An upper bound for the rejection probability based on this construction can be expressed to evaluate the efficiency of the proposal before sampling. A method to partition the support is considered where regions are bifurcated based on their contribution to the bound. Examples based on the von Mises Fisher distribution and Gaussian Process regression are provided to illustrate the method.

翻译：许多统计应用中出现的分布可以表示为加权密度的形式：基础密度与非负权重函数的乘积。从这类分布中生成样本可能并非易事，且常涉及难以计算的归一化常数。拒绝采样可用于生成精确样本，但需制定合适的提议分布。为实用起见，提议分布必须既便于采样，又不会过于频繁地拒绝候选样本。一种著名的提议分布设计方法涉及将目标密度分解为有限混合形式，其分量可能对应于支撑集的划分。本研究考虑了这样一种构造方法，重点关注权重函数的优超。当自适应拒绝采样及相关算法的假设条件不满足时，该方法可能具有适用性。基于该构造的拒绝概率上界可在采样前用于评估提议分布的效率。本文还探讨了一种支撑集划分方法，其中区域根据其对上界的贡献进行二分。通过冯·米塞斯-费舍尔分布和高斯过程回归的示例来说明该方法。