Bayesian methods
Hamiltonian Monte Carlo
Hamiltonian Monte Carlo (HMC) is a gradient-based Markov chain Monte Carlo algorithm that uses the geometry of the log-posterior surface to make large, informed jumps through parameter space instead of the small random steps of classical MCMC. Originally introduced for lattice field theory by Duane, Kennedy, Pendleton, and Roweth (1987) under the name Hybrid Monte Carlo, and brought into mainstream statistics by Radford Neal's authoritative 2011 chapter, HMC is today the default sampler in Stan and PyMC and is widely regarded as the state-of-the-art engine for Bayesian posterior inference in high-dimensional models.
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Sources
- Duane, S., Kennedy, A. D., Pendleton, B. J., & Roweth, D. (1987). Hybrid Monte Carlo. Physics Letters B, 195(2), 216–222. DOI: 10.1016/0370-2693(87)91197-X ↗
- Neal, R. M. (2011). MCMC using Hamiltonian dynamics. In S. Brooks, A. Gelman, G. L. Jones, & X.-L. Meng (Eds.), Handbook of Markov Chain Monte Carlo (pp. 116–162). Chapman and Hall/CRC. ISBN: 978-1420079418 ↗
- Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2013). Bayesian Data Analysis (3rd ed.). CRC Press. ISBN: 978-1439840955
Related methods
Referenced by
Dynamic Hamiltonian Monte CarloDynamic Sequential Monte CarloGibbs SamplingHamiltonian Monte Carlo with Measurement ErrorHamiltonian Monte Carlo with Missing DataHierarchical Hamiltonian Monte CarloHierarchical Markov Chain Monte CarloMCMC for Model ComparisonMCMC with missing dataMetropolis-Hastings AlgorithmMultilevel Gibbs SamplingMultilevel Hamiltonian Monte CarloMultilevel MCMCNo-U-Turn SamplerRobust Hamiltonian Monte CarloRobust Markov chain Monte CarloRobust Particle FilterRobust Sequential Monte CarloSequential Monte CarloSlice SamplingSpatial MCMCTime series MCMC