  Leveraging the coherent exploration of Hamiltonian flow, Hamiltonian Monte
Carlo produces computationally efficient Monte Carlo estimators, even with
respect to complex and high-dimensional target distributions. When confronted
with data-intensive applications, however, the algorithm may be too expensive
to implement, leaving us to consider the utility of approximations such as data
subsampling. In this paper I demonstrate how data subsampling fundamentally
compromises the efficient exploration of Hamiltonian flow and hence the
scalable performance of Hamiltonian Monte Carlo itself.

Methodology