  Hamiltonian Monte Carlo has proven a remarkable empirical success, but only
recently have we begun to develop a rigorous understanding of why it performs
so well on difficult problems and how it is best applied in practice.
Unfortunately, that understanding is confined within the mathematics of
differential geometry which has limited its dissemination, especially to the
applied communities for which it is particularly important. In this review I
provide a comprehensive conceptual account of these theoretical foundations,
focusing on developing a principled intuition behind the method and its optimal
implementations rather of any exhaustive rigor. Whether a practitioner or a
statistician, the dedicated reader will acquire a solid grasp of how
Hamiltonian Monte Carlo works, when it succeeds, and, perhaps most importantly,
when it fails.
