Key word

  • HMC

参考文献

※随時更新．

基本

  • R. M. Neal, Mcmc using hamiltonian dynamics, in HANDBOOK OF MARKOV CHAIN659, MONTE CARLO, Chapman & Hall/CRC., 2011, pp. 113–162
    • 有名なHMCのreview

Geometric Ergodicity

  • S. Livingstone, M. Betancourt, S. Byrne, and M. Girolami, On the geometric ergodicity of hamiltonian monte carlo, 2016, https://arxiv.org/abs/1601.08057

MCMC

  • Sean P Meyn and Richard L Tweedie, Markov chains and stochastic stability, Springer Science & Business Media, 2005.
  • Gareth O. Roberts and Jeffrey S. Rosenthal, General state space markov chains and mcmc algorithms. Probability Surveys, 2004.
  • D. Rudolf, Explicit error bounds for markov chain monte carlo, Dissertationes Math., 2012

Integrator

  • Bou-Rabee et al., Geometric Integrators and the Hamiltonian Monte Carlo Algorithm, Acta Numerica, 2018
    • HMCのための数値スキームについてreviewしている．
  • Hairer et al., Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations, Springer, 2006
    • 構造保存型スキームの本
  • E. Marsden and M. West, Discrete mechanics and variational integrators, Acta Numer., 2001
    • 離散変分原理に関するreview．
    • 多様体上に制限された問題も扱っている．

多様体・制約付き (manifold/constrained)

  • M. Brubaker, M. Salzmann, and R. Urtasun, A family of mcmc methods on implicitly defined manifolds, in Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics, 2012