  The performance of Hamiltonian Monte Carlo (HMC) sampler depends critically
on some algorithm parameters such as the total integration time and the
numerical integration stepsize. The parameter tuning is particularly
challenging when the mass matrix of the HMC sampler is adapted. We propose in
this work a Kolmogorov-Sinai entropy (KSE) based design criterion to optimize
these algorithm parameters, which can avoid some potential issues in the often
used jumping-distance based measures. For near-Gaussian distributions, we are
able to derive the optimal algorithm parameters with respect to the KSE
criterion analytically. As a byproduct the KSE criterion also provides a
theoretical justification for the need to adapt the mass matrix in HMC sampler.
Based on the results, we propose an adaptive HMC algorithm, and we then
demonstrate the performance of the proposed algorithm with numerical examples.
