Methoden vergleichen

	Robust Hamiltonian Monte Carlo	Variationelle Inferenz
Fachgebiet	Bayes-Statistik	Bayes-Statistik
Familie	Bayesian methods	Bayesian methods
Entstehungsjahr	2010s–2020s	1999
Urheber	Livingstone, Zanella and related researchers building on Duane et al. (1987)	Jordan, Ghahramani, Jaakkola & Saul
Typ	Robust MCMC sampler	Approximate Bayesian inference
Wegweisende Quelle	Livingstone, S. & Zanella, G. (2022). The Barker proposal: combining robustness and efficiency in gradient-based MCMC. Journal of the Royal Statistical Society: Series B, 84(2), 496–523.	Jordan, M. I., Ghahramani, Z., Jaakkola, T. S., & Saul, L. K. (1999). An introduction to variational methods for graphical models. Machine Learning, 37(2), 183–233.
Aliasnamen	Robust HMC, heavy-tailed HMC, geometric-ergodic HMC, outlier-robust HMC	VI, variational Bayes, VB, mean-field variational inference
Verwandt	4	4
Zusammenfassung	Robust Hamiltonian Monte Carlo (Robust HMC) is a family of extensions to standard HMC designed to maintain geometric ergodicity and sampling efficiency when the posterior has heavy tails, strong curvature variation, or near-degenerate geometry. By modifying the kinetic energy, mass matrix, or proposal mechanism, these methods ensure reliable exploration of difficult posteriors that defeat the standard NUTS/HMC sampler.	Variational inference (VI) is a family of techniques that turn Bayesian posterior computation into an optimisation problem. Instead of drawing samples from the exact posterior — as Markov chain Monte Carlo does — VI posits a simpler, tractable family of distributions and finds the member of that family closest to the true posterior by maximising the evidence lower bound (ELBO). Introduced in its modern graphical-model form by Jordan, Ghahramani, Jaakkola and Saul (1999) and given a comprehensive statistical treatment by Blei, Kucukelbir and McAuliffe (2017), VI is now the standard scalable inference engine in probabilistic machine learning.