论文标题
截短的对数凸线分布的可扩展随机数生成
Scalable random number generation for truncated log-concave distributions
论文作者
论文摘要
逆变换采样是一种生成非均匀分布的随机数的异常通用方法，但是在模拟极度截断的分布时可能是不稳定的。许多著名的概率模型共享一个名为Log-Concavity的属性，该属性不受截断的影响，因此可以使用Devroye的方法通过拒绝采样来模拟它们。该采样器基于拒绝，因此比逆变换更稳定，并使用一个非常简单的信封，其接受率保证至少为20 \％。本文的目的是三重：首先，警告截断分布中错误模拟的风险；其次，激励更广泛地使用拒绝抽样来减轻问题；最后，在日志concave发行时，激励Devroye的自动方法作为实用标准。我们通过基于某些Tweedie分布的模拟来说明该提案，以便它们在回归分析中的相关性。
Inverse transform sampling is an exceptionally general method to generate non-uniform-distributed random numbers, but can be rather unstable when simulating extremely truncated distributions. Many famous probability models share a property called log-concavity, which is not affected by truncation, so they can all be simulated via rejection sampling using Devroye's approach. This sampler is based on rejection and thus more stable than inverse transform, and uses a very simple envelope whose acceptance rate is guaranteed to be at least 20\%. The aim of this paper is threefold: firstly, to warn against the risk of wrongly simulating from truncated distributions; secondly, to motivate a more extensive use of rejection sampling to mitigate the issues; lastly, to motivate Devroye's automatic method as a practical standard in the case of log-concave distributions. We illustrate the proposal by means of simulations based on some Tweedie distributions, for their relevance in regression analysis.
