• Corpus ID: 88514713

A Conceptual Introduction to Hamiltonian Monte Carlo

@article{Betancourt2017ACI,
  title={A Conceptual Introduction to Hamiltonian Monte Carlo},
  author={Michael Betancourt},
  journal={arXiv: Methodology},
  year={2017}
}
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… 
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References

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The formal foundations of the algorithm are developed through the construction of measures on smooth manifolds, and how the theory naturally identifies efficient implementations and motivates promising generalizations are demonstrated.
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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
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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 underlying
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
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