AI 中文总结
针对多元期望分位数分布，提出一种基于仿射白化、极坐标分解和双曲变换的拒绝采样器，使接受概率均匀地不低于0.632，适用于任意维度和不对称参数。
AI 中文摘要
多元期望分位数分布是Arbel等人于2023年提出的多元高斯分布的“尖峰”扰动。该研究最初提出的拒绝采样器虽然有效，但其接受概率在高维和强不对称极限下可能严重退化。我们给出一个简单替代方案。经过仿射白化和极坐标分解，采样问题精确简化为单变量分布，再通过额外的双曲变量替换，该分布表现为对数凹性，从而适用Devroye的通用且一致高效的构造方法。由此得到的精确采样器，其接受概率至少为$1 - \exp \left( -1 \right) = 0.632120 \ldots$，对维度和所有可允许的不对称参数一致成立。
英文摘要
The multivariate expectile-based distribution is a `spiked' perturbation of a multivariate Gaussian distribution, proposed by Arbel et al. in 2023. The rejection sampler proposed for this distribution in the initial work is valid, but its acceptance probability can degenerate badly both in high dimension and in the strongly asymmetric limit. We give a simple alternative. After affine whitening and a polar decomposition, the sampling problem reduces exactly to a univariate distribution, and an additional hyperbolic change of variables exhibits this distribution as log-concave, so that a universal and uniformly efficient construction of Devroye applies. The resulting exact sampler therefore enjoys an acceptance probability of at least $1 - \exp \left( -1 \right) = 0.632120 \ldots$, uniformly over the dimension and all admissible asymmetry parameters.
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