  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.
