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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References

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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 underlyingExpand
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 suitableExpand
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 bothExpand
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 ofExpand
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 discretizationExpand
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 whenExpand
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 theExpand
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 thatExpand
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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