This article introduces the Modified Parameterized Leapfrog Hamiltonian Monte Carlo (MPL-HMC) method, a novel extension of HMC addressing key limitations through tunable integration parameters $α(δt)$ and $β(δt)$, enabling controlled perturbations to Hamiltonian dynamics. Theoretical analysis demonstrates MPL-HMC maintains approximate detailed balance. Extensive empirical evaluation reveals systematic performance improvements. The damping variant ($α_2=-0.1$, $β_2=-0.05$) achieves a 14-fold increase in effective sample size for Neal's funnel and 27\% better efficiency for pharmacokinetic models. The anti-damping variant ($α_2=0.1$, $β_2=0.05$) achieves $\hat{R}=1.026$ for Bayesian neural networks versus $\hat{R}=1.981$ for standard HMC. We introduce aggressive MPL-HMC for multimodal distributions, employing extreme parameters ($α_2=8.0$--$15.0$, $β_2=5.0$--$8.0$) with enhanced sampling to achieve full mode exploration where standard methods fail. All variants maintain computational efficiency identical to standard HMC while providing systematic control over damping, exploration, stability, and accuracy. The article provides rigorous mathematical foundations, implementation specifications, parameter tuning strategies, and comprehensive performance comparisons, extending HMC's applicability to previously challenging domains.

翻译：本文介绍了改进的参数化蛙跳哈密顿蒙特卡洛（MPL-HMC）方法，这是对HMC的一种新颖扩展，它通过可调的积分参数$α(δt)$和$β(δt)$解决了HMC的关键局限性，从而能够对哈密顿动力学进行受控扰动。理论分析表明MPL-HMC保持了近似的细致平衡。广泛的实证评估揭示了系统性的性能提升。阻尼变体（$α_2=-0.1$，$β_2=-0.05$）在Neal漏斗分布上实现了有效样本量14倍的提升，在药代动力学模型上实现了27%的效率提升。反阻尼变体（$α_2=0.1$，$β_2=0.05$）在贝叶斯神经网络上达到$\hat{R}=1.026$，而标准HMC为$\hat{R}=1.981$。我们针对多峰分布引入了激进MPL-HMC，采用极端参数（$α_2=8.0$--$15.0$，$β_2=5.0$--$8.0$）并结合增强采样，实现了在标准方法失效情况下对所有模态的完整探索。所有变体在保持与标准HMC相同计算效率的同时，提供了对阻尼、探索性、稳定性和准确性的系统性控制。本文提供了严格的数学基础、实现规范、参数调优策略以及全面的性能比较，从而将HMC的适用性扩展到了先前具有挑战性的领域。