Abstract
As already highlighted in this book, HMC has two main practical issues. The first is the deterioration in acceptance rates as the system size increases, and the second is its sensitivity to two user-specified parameters: the step size and trajectory length. The former issue is addressed by sampling from an integrator-dependent modified or shadow density and compensating for the induced bias via importance sampling. The latter issue is addressed by adaptively setting the HMC parameters, with the state-of-art method being the NUTS algorithm. The automatic tuning of parameters of shadow Hamiltonian methods is yet to be considered in the literature. In this chapter, we combine the benefits of NUTS with those attained by sampling from the shadow density by adaptively setting the trajectory length and step size of S2HMC to make it more accessible to non-expert users. This leads to a new algorithm which we refer to as adaptive S2HMC, that shows improved performance over S2HMC and NUTS across various targets and leaves the target density invariant.
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