ABSTRACT
The theory and algorithms increase in sophistication substantially for Hamiltonian Monte Carlo (HMC). Thus, despite efforts to communicate an intuition about HMC to ecologists, the theory and procedure are poorly understood by most users of automated HMC software. The Hamiltonian trajectory is strikingly similar to a continuous-time animal movement model. The path of the Hamiltonian trajectory can be expressed as a set of differential equations. The concept that distinguishes HMC from conventional Metropolis-Hastings (M-H) updates is the Hamiltonian trajectory. The use of the Hamiltonian trajectory to obtain M-H proposals is straightforward. HMC algorithms require nested “for” loops because simulating the Hamiltonian trajectory requires a loop that is inside the larger Markov chain Monte Carlo loop. The chapter focuses on a very simple form of HMC algorithm for a simple model where it was straightforward to tune the proposals so that they provide well-mixed Markov chains.
