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：本文提出一种通用方法，用于在解析难以处理的受限支撑分布中进行高效数值模拟。该方法基于广义随机哈密顿蒙特卡洛过程，并结合随机转移核在约束域边界处对哈密顿流进行适当调整，确保其始终保持在域内。受限GRHMC过程的数值实现充分利用了随机转移核的稀疏性及约束条件的特定结构，使得所提方法在数值上精确、计算快速，即使在高维应用中也能有效运行。我们通过在真实数据集上应用多个具有挑战性参数域约束的贝叶斯模型后验分布来展示该方法。基于GRHMC过程高效探索复杂高维后验分布的能力，所提方法扩展了可通过标准马尔可夫链蒙特卡洛方法分析的贝叶斯模型范围。因此，该方法能推动具有实用约束先验的贝叶斯模型的发展与应用，这类模型用现有方法难以处理。本文附有R软件包（\url{https://github.com/torekleppe/pdmphmc}），可针对任意目标分布与域约束自动实现GRHMC过程。