Hamiltonian Monte Carlo has proven a remarkable empirical success, but only
recently have we begun to develop a rigorous under- standing of why it performs
so well on difficult problems and how it is best applied in practice.
Unfortunately, that understanding is con- fined 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 ex- haustive 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.