2016/01/02 by Michael Betancourt, Betancourt, Michael
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #Computation (stat.CO) #FOS: Computer and information sciences #Markov Chains and Monte Carlo Methods #Methodology (stat.ME) #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.1601.00225
openalex publication_date 2016/01/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
By leveraging the natural geometry of a smooth probabilistic system, Hamiltonian Monte Carlo yields computationally efficient Markov Chain Monte Carlo estimation. At least provided that the algorithm is sufficiently well-tuned. In this paper I show how the geometric foundations of Hamiltonian Monte Carlo implicitly identify the optimal choice of these parameters, especially the integration time. I then consider the practical consequences of these principles in both existing algorithms and a new implementation called Exhaustive Hamiltonian Monte Carlo before demonstrating the utility of these ideas in some illustrative examples.