带垂直加权条带的拒绝采样
Rejection Sampling with Vertical Weighted Strips
AI总结：
针对加权密度分布采样难的问题，提出基于权重函数优控、按上界贡献划分支撑集的拒绝采样方法，可在自适应拒绝采样假设不满足时使用，还能预评估采样效率，并用von Mises Fisher分布实例验证了框架。
摘要：
统计应用中出现的许多分布都可以表示为加权密度的形式：即基密度与非负权重函数的乘积。从这类分布中生成随机变量可能并非易事，还可能涉及难以处理的归一化常数。拒绝采样可用于生成精确抽样，但需要构建合适的提议分布。要具备实际实用性，提议分布必须既便于采样，又不会过于频繁地拒绝候选抽样。设计提议分布的一种知名方法是将目标密度分解为有限混合分布，其分量可对应支撑集的一个划分。本文研究了一种聚焦于权重函数优控的此类构造方法。当自适应拒绝采样及相关算法的假设条件不满足时，该方法可能适用。基于这种构造的拒绝概率上界可以被表示出来，用于在采样前评估提议分布的效率。本文还研究了一种支撑集划分方法，即根据各区域对该上界的贡献对其进行分叉。本文还基于von Mises Fisher分布给出了若干应用实例，以说明该框架的有效性。
英文摘要：
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. Several applications based on the von Mises Fisher distribution are presented to illustrate the framework.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
