Hamiltonian Monte Carlo

In mathematics and physics, Hamiltonian Monte Carlo algorithm (originally known as hybrid Monte Carlo), is a Markov chain Monte Carlo method for obtaining a sequence of random samples from a probability distribution for which direct sampling is difficult. This sequence can be used to approximate the distribution (i.e., to generate a histogram), or to compute an integral (such as an expected value).

It differs from the Metropolis–Hastings algorithm by reducing the correlation between successive sampled states by using a Hamiltonian evolution between states and additionally by targeting states with a higher acceptance criteria than the observed probability distribution. This causes it to converge more quickly to the absolute probability distribution. It was devised by Simon Duane, A.D. Kennedy, Brian Pendleton and Duncan Roweth in 1987,[1] for calculations in lattice quantum chromodynamics.

See also

Notes

  1. ↑ Duane, Simon; Kennedy, A.D.; Pendleton, Brian J.; Roweth, Duncan (3 September 1987). "Hybrid Monte Carlo". Physics Letters B. 195 (2): 216–222. Bibcode:1987PhLB..195..216D. doi:10.1016/0370-2693(87)91197-X.

References

  • Neal, Radford M (2011). "MCMC Using Hamiltonian Dynamics" (PDF). In Steve Brooks; Andrew Gelman; Galin L. Jones; Xiao-Li Meng. Handbook of Markov Chain Monte Carlo. Chapman and Hall/CRC. ISBN 9781420079418.
  • Betancourt, Michael (2018). "A Conceptual Introduction to Hamiltonian Monte Carlo". arXiv:1701.02434. Bibcode:2017arXiv170102434B.
  • Betancourt, Michael. "Efficient Bayesian inference with Hamiltonian Monte Carlo". MLSS Iceland 2014 – via YouTube.
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