Corpus ID: 88514713

A Conceptual Introduction to Hamiltonian Monte Carlo

@article{Betancourt2017ACI,
  title={A Conceptual Introduction to Hamiltonian Monte Carlo},
  author={M. Betancourt},
  journal={arXiv: Methodology},
  year={2017}
}
  • M. Betancourt
  • Published 2017
  • Computer Science, Mathematics
  • arXiv: Methodology
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… Expand
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511 Citations
Highly Influential Citations
74
Background Citations
173
Methods Citations
191
Results Citations
2

511 Citations

Citation Type

Citation Type

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A theoretical basis for the use of non-canonical Hamiltonian dynamics in MCMC is established, and a symplectic, leapfrog-like integrator is constructed allowing for the implementation of magnetic HMC. Expand
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  • 2018
Hamiltonian Dynamics Monte Carlo is a popular method used in simulating complicated distribution. The performance of HMC highly depends on geometry of the momentum-state dual space; we investigate… Expand
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Hamiltonian Monte Carlo is a popular sampling technique for smooth target densities. The scale lengths of the target have long been believed to influence sampling efficiency, but quantitative… Expand
Discontinuous Hamiltonian Monte Carlo for Probabilistic Programs
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References

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Optimizing The Integrator Step Size for Hamiltonian Monte Carlo
Hamiltonian Monte Carlo can provide powerful inference in complex statistical problems, but ultimately its performance is sensitive to various tuning parameters. In this paper we use the underlying… Expand
CURVATURE AND CONCENTRATION OF HAMILTONIAN MONTE CARLO IN HIGH DIMENSIONS
In this article, we analyze Hamiltonian Monte Carlo (HMC) by placing it in the setting of Riemannian geometry using the Jacobi metric, so that each step corresponds to a geodesic on a suitable… Expand
On the Geometric Ergodicity of Hamiltonian Monte Carlo
We establish general conditions under which Markov chains produced by the Hamiltonian Monte Carlo method will and will not be geometrically ergodic. We consider implementations with both… Expand
MCMC Using Hamiltonian Dynamics
Hamiltonian dynamics can be used to produce distant proposals for the Metropolis algorithm, thereby avoiding the slow exploration of the state space that results from the diffusive behaviour of… Expand
Generalizing the No-U-Turn Sampler to Riemannian Manifolds
Hamiltonian Monte Carlo provides efficient Markov transitions at the expense of introducing two free parameters: a step size and total integration time. Because the step size controls discretization… Expand
Riemann manifold Langevin and Hamiltonian Monte Carlo methods
The paper proposes Metropolis adjusted Langevin and Hamiltonian Monte Carlo sampling methods defined on the Riemann manifold to resolve the shortcomings of existing Monte Carlo algorithms when… Expand
Diagnosing Suboptimal Cotangent Disintegrations in Hamiltonian Monte Carlo
When properly tuned, Hamiltonian Monte Carlo scales to some of the most challenging high-dimensional problems at the frontiers of applied statistics, but when that tuning is suboptimal the… Expand
Control functionals for Monte Carlo integration
Summary A non-parametric extension of control variates is presented. These leverage gradient information on the sampling density to achieve substantial variance reduction. It is not required that… Expand
A General Metric for Riemannian Hamiltonian Monte Carlo
A General Metric for Riemannian Hamiltonian Monte Carlo Michael Betancourt University College London August 30th, 2013 I’m going to talk about probability and geometry, but not information geometry!… Expand
Numerical Integrators for the Hybrid Monte Carlo Method
TLDR
Limited, proof-of-concept numerical experiments suggest that the new integrators constructed may provide an improvement on the efficiency of the standard Verlet method, especially in problems with high dimensionality. Expand
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