The hybrid Monte Carlo (HMC) algorithm is arguably the most efficient sampling method for general probability distributions of continuous variables. Together with exact Fourier acceleration (EFA) the HMC becomes equivalent to direct sampling for quadratic actions $S(x)=\frac12 x^\mathsf{T} M x$ (i.e. normal distributions $x\sim \mathrm{e}^{-S(x)}$), only perturbatively worse for perturbative deviations of the action from the quadratic case, and it remains viable for arbitrary actions. In this work the most recent improvements of the HMC including EFA and radial updates are collected into a numerical recipe.

翻译：混合蒙特卡洛（HMC）算法无疑是连续变量一般概率分布最高效的采样方法。结合精确傅里叶加速（EFA）技术，HMC在二次型作用量 $S(x)=\frac12 x^\mathsf{T} M x$（即正态分布 $x\sim \mathrm{e}^{-S(x)}$）情形下等价于直接采样，对于作用量偏离二次型的微扰情形仅产生微扰阶次的性能衰减，且适用于任意形式的作用量。本文系统整合了包括EFA与径向更新在内的HMC最新进展，形成一套完整的数值计算方案。