Last update: 20241204

The Markov-chain Monte Carlo (MCMC) sampler gallery

This page is cloned from Chi Feng at https://github.com/chi-feng/mcmc-demo to have an important references for MCMC samplers.

The following demo shows a multimodal dataset with Gibbs sampling.

Click on an algorithm below to view interactive demo:

• Random Walk Metropolis Hastings
• Adaptive Metropolis Hastings [1]
• Hamiltonian Monte Carlo [2]
• No-U-Turn Sampler [2]
• Metropolis-adjusted Langevin Algorithm (MALA) [3]
• Hessian-Hamiltonian Monte Carlo (H2MC) [4]
• Gibbs Sampling
• Stein Variational Gradient Descent (SVGD) [5]
• Nested Sampling with RadFriends (RadFriends-NS) [6]
• Differential Evolution Metropolis (Z) [7]
• Microcanonical Hamiltonian Monte Carlo [8]

View the source code on GitHub: https://github.com/chi-feng/mcmc-demo.

References

• [1] H. Haario, E. Saksman, and J. Tamminen, An adaptive Metropolis algorithm (2001)
• [2] M. D. Hoffman, A. Gelman, The No-U-Turn Sampler: Adaptively Setting Path Lengths in Hamiltonian Monte Carlo (2011)
• [3] G. O. Roberts, R. L. Tweedie, Exponential Convergence of Langevin Distributions and Their Discrete Approximations (1996)
• [4] Li, Tzu-Mao, et al. Anisotropic Gaussian mutations for metropolis light transport through Hessian-Hamiltonian dynamics ACM Transactions on Graphics 34.6 (2015): 209.
• [5] Q. Liu, et al. Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithm Advances in Neural Information Processing Systems. 2016.
• [6] J. Buchner A statistical test for Nested Sampling algorithms Statistics and Computing. 2014.
• [7] Cajo J. F. ter Braak & Jasper A. Vrugt Differential Evolution Markov Chain with snooker updater and fewer chains Statistics and Computing. 2008.
• [8] Jakob Robnik, G. Bruno De Luca, Eva Silverstein, Uroš Seljak Microcanonical Hamiltonian Monte Carlo