论文标题
HDTG：用于高维截短的正常模拟的R包装
hdtg: An R package for high-dimensional truncated normal simulation
论文作者
论文摘要
在各种统计应用中需要从多元截短的正态分布（MTN）模拟，但在高维度中仍然具有挑战性。当前可用的算法及其实现通常会在参数数量超过几百时失败。为了提供一种一般的计算工具来有效地从高维MTN进行采样，我们引入了HDTG软件包，该软件包实现了两种最先进的模拟算法：Harmonic Hamiltonian Monte Carlo（Harmonic-HMC）和Zigzag Hamiltonian Monte Carlo（Zigzag-HMC）（Zigzag-HMC）。两种算法在具有硬边界约束的二次势能下利用了哈密顿动力学的分析解，导致无排斥的方法。我们将它们的效率与MTN模拟的另一种最新算法进行比较，即Minimax倾斜接受抽样器（MET）。这三种方法的运行时间在很大程度上取决于基本的多元正常相关结构。曲折-HMC和谐波-HMC在所有测试的3,600秒内都获得了100个有效样品，尺寸范围从100到1,600，而MET在几个高维示例中很难。我们提供有关如何在给定情况下选择适当方法的指导，并说明HDTG的使用情况。
Simulating from the multivariate truncated normal distribution (MTN) is required in various statistical applications yet remains challenging in high dimensions. Currently available algorithms and their implementations often fail when the number of parameters exceeds a few hundred. To provide a general computational tool to efficiently sample from high-dimensional MTNs, we introduce the hdtg package that implements two state-of-the-art simulation algorithms: harmonic Hamiltonian Monte Carlo (harmonic-HMC) and zigzag Hamiltonian Monte Carlo (Zigzag-HMC). Both algorithms exploit analytical solutions of the Hamiltonian dynamics under a quadratic potential energy with hard boundary constraints, leading to rejection-free methods. We compare their efficiencies against another state-of-the-art algorithm for MTN simulation, the minimax tilting accept-reject sampler (MET). The run-time of these three approaches heavily depends on the underlying multivariate normal correlation structure. Zigzag-HMC and harmonic-HMC both achieve 100 effective samples within 3,600 seconds across all tests with dimension ranging from 100 to 1,600, while MET has difficulty in several high-dimensional examples. We provide guidance on how to choose an appropriate method for a given situation and illustrate the usage of hdtg.
