Authors

Michael Betancourt, Simon Byrne, Sam Livingstone, Mark Girolami

Abstract

Although Hamiltonian Monte Carlo has proven an empirical success, the lack of a rigorous theoretical understanding of the algorithm has in many ways impeded both principled developments of the method and use of the algorithm in practice. In this paper we develop the formal foundations of the algorithm through the construction of measures on smooth manifolds, and demonstrate how the theory naturally identifies efficient implementations and motivates promising generalizations.

Citation

  • Journal: Bernoulli
  • Year: 2017
  • Volume: 23
  • Issue: 4A
  • Pages:
  • Publisher: Bernoulli Society for Mathematical Statistics and Probability
  • DOI: 10.3150/16-bej810

BibTeX

@article{Betancourt_2017,
  title={{The geometric foundations of Hamiltonian Monte Carlo}},
  volume={23},
  ISSN={1350-7265},
  DOI={10.3150/16-bej810},
  number={4A},
  journal={Bernoulli},
  publisher={Bernoulli Society for Mathematical Statistics and Probability},
  author={Betancourt, Michael and Byrne, Simon and Livingstone, Sam and Girolami, Mark},
  year={2017}
}

Download the bib file

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