We propose a generic approach for numerically efficient simulation from analytically intractable distributions with constrained support. Our approach relies upon Generalized Randomized Hamiltonian Monte Carlo (GRHMC) processes and combines these with a randomized transition kernel that appropriately adjusts the Hamiltonian flow at the boundary of the constrained domain, ensuring that it remains within the domain. The numerical implementation of this constrained GRHMC process exploits the sparsity of the randomized transition kernel and the specific structure of the constraints so that the proposed approach is numerically accurate, computationally fast and operational even in high-dimensional applications. We illustrate this approach with posterior distributions of several Bayesian models with challenging parameter domain constraints in applications to real-word data sets. Building on the capability of GRHMC processes to efficiently explore otherwise challenging and high-dimensional posteriors, the proposed method expands the set of Bayesian models that can be analyzed by using the standard Markov-Chain Monte-Carlo (MCMC) methodology, As such, it can advance the development and use of Bayesian models with useful constrained priors, which are difficult to handle with existing methods. The article is accompanied by an R-package (\url{https://github.com/torekleppe/pdmphmc}), which allows for automatically implementing GRHMC processes for arbitrary target distributions and domain constraints.

翻译：我们提出了一种通用方法，用于在约束支撑条件下对解析上难以处理的分布进行高效数值模拟。该方法基于广义随机化哈密顿蒙特卡洛（GRHMC）过程，并将其与随机转移核相结合，在约束区域的边界处适当调整哈密顿流，确保其始终保持在区域内。该约束GRHMC过程的数值实现利用了随机转移核的稀疏性和约束的特殊结构，从而使所提方法具有数值精度高、计算速度快的特点，即使在维数较高的应用中也能稳定运行。我们通过多个贝叶斯模型的真实数据集后验分布进行验证，这些模型具有极具挑战性的参数约束域。基于GRHMC过程能够高效探索原本困难的高维后验分布这一优势，所提方法扩展了可通过标准马尔可夫链蒙特卡洛（MCMC）方法分析的贝叶斯模型集合。因此，该方法能推动具有实用约束先验（而现有方法难以处理此类先验）的贝叶斯模型的发展与应用。本文配套提供R语言软件包（\url{https://github.com/torekleppe/pdmphmc}），可自动为任意目标分布和域约束实现GRHMC过程。