We introduce a Hamiltonian Monte Carlo (HMC) methodology based on a randomized selection of integration times, referred to as eHMC, where "e" stands for empirical. The approach relies on an offline calibration phase that leverages importance sampling to construct an empirical distribution on discretization parameters, thereby eliminating the need for manual burn-in diagnostics and online adaptation. The proposal distribution used in the calibration stage is obtained via a Population Monte Carlo scheme combined with tempering and flexible parametric variational families such as normalizing flows. The resulting algorithm defines a mixture of HMC kernels with a fixed mixing distribution, preserving the target distribution. Numerical experiments on benchmarks demonstrate that eHMC achieves competitive or improved efficiency compared to the No-U-Turn Sampler (NUTS) when accounting for computational cost. These results suggest that offline calibration combined with randomized integration schemes provides a viable alternative to adaptive HMC methods.

翻译：我们提出一种基于积分时间随机选择的哈密顿蒙特卡洛(HMC)方法，称为eHMC（"e"代表经验性）。该方法依赖于离线校准阶段，利用重要性采样构建离散化参数的经验分布，从而消除手动燃烧诊断与在线自适应需求。校准阶段使用的提议分布通过结合退火策略与柔性参数化变分族（如归一化流）的群蒙特卡洛方案获得。所得算法定义了混合分布固定的HMC核混合体，保持目标分布不变。数值基准实验表明，在考虑计算成本时，eHMC相比无回转采样器(NUTS)具有相当或更优的效率。这些结果表明，离线校准结合随机化积分方案为自适应HMC方法提供了可行替代方案。