Elliptical slice sampling, when adapted to linearly truncated multivariate normal distributions, is a rejection-free Markov chain Monte Carlo method. At its core, it requires analytically constructing an ellipse-polytope intersection. The main novelty of this paper is an algorithm that computes this intersection in $\mathcal{O}(m \log m)$ time, where $m$ is the number of linear inequality constraints representing the polytope. We show that an implementation based on this algorithm enhances numerical stability, speeds up running time, and is easy to parallelize for launching multiple Markov chains.

翻译：椭圆切片采样在适应于线性截断多元正态分布时，是一种无拒绝的马尔可夫链蒙特卡洛方法。其核心在于需要解析地构造一个椭圆-多面体交集。本文的主要创新在于提出了一种算法，该算法能以 $\mathcal{O}(m \log m)$ 的时间复杂度计算此交集，其中 $m$ 是表示多面体的线性不等式约束的数量。我们证明，基于此算法的实现提高了数值稳定性，加快了运行时间，并且易于并行化以启动多个马尔可夫链。