পদ্ধতির তুলনা করুন

	হ্যামিলটোনিয়ান মন্টি কার্লো	মার্কভ চেইন মন্টি কার্লো (MCMC)	ভ্যারিয়েশনাল ইনফারেন্স (Variational Inference)
ক্ষেত্র	বেইসীয়	বেইসীয়	বেইসীয়
পরিবার	Bayesian methods	Bayesian methods	Bayesian methods
উদ্ভবের বছর	1987	—	1999
প্রবর্তক	—	—	Jordan, Ghahramani, Jaakkola & Saul
ধরন	Gradient-based Markov chain Monte Carlo sampler	Posterior sampling algorithm	Approximate Bayesian inference
মৌলিক উৎস	Duane, S., Kennedy, A. D., Pendleton, B. J., & Roweth, D. (1987). Hybrid Monte Carlo. Physics Letters B, 195(2), 216–222.	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	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.
অপর নাম	HMC, Hybrid Monte Carlo, NUTS, No-U-Turn Sampler	markov chain monte carlo, MCMC sampling, MCMC (Markov Zinciri Monte Carlo)	VI, variational Bayes, VB, mean-field variational inference
সম্পর্কিত	3	3	4
সারসংক্ষেপ	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.	Markov Chain Monte Carlo (MCMC) is a family of computational algorithms for sampling from complex probability distributions, most commonly the posterior distributions that arise in Bayesian inference. Rather than computing posteriors analytically — which is rarely possible for realistic models — MCMC constructs a Markov chain whose stationary distribution is the target posterior and draws dependent samples from it, enabling full probabilistic inference for virtually any model.	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.