Three approaches for adaptively tuning diagonal scale matrices for HMC are discussed and compared. The common practice of scaling according to estimated marginal standard deviations is taken as a benchmark. Scaling according to the mean log-target gradient (ISG), and a scaling method targeting that the frequency of when the underlying Hamiltonian dynamics crosses the respective medians should be uniform across dimensions, are taken as alternatives. Numerical studies suggest that the ISG method leads in many cases to more efficient sampling than the benchmark, in particular in cases with strong correlations or non-linear dependencies. The ISG method is also easy to implement, computationally cheap and would be relatively simple to include in automatically tuned codes as an alternative to the benchmark practice.

翻译：讨论了三种自适应调整HMC对角尺度矩阵的方法并进行了比较。以根据估计的边际标准差进行缩放这一常见做法作为基准。将根据对数目标梯度均值（ISG）进行缩放，以及一种旨在使底层哈密顿动力学穿过各自中位数的频率在各维度上均匀的缩放方法作为替代方案。数值研究表明，ISG方法在许多情况下能比基准方法实现更高效的采样，尤其是在存在强相关性或非线性依赖关系的场景中。ISG方法还易于实现，计算成本低，并且相对容易作为基准实践的替代方案纳入自动调整代码中。