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	Expectation Propagation (EP)	Laplace-approximation	Markov Chain Monte Carlo (MCMC)
Ämnesområde	Bayesiansk statistik	Bayesiansk statistik	Bayesiansk statistik
Familj	Bayesian methods	Bayesian methods	Bayesian methods
Ursprungsår	2001	1986	—
Upphovsperson	Thomas P. Minka	Pierre-Simon Laplace (1774); Bayesian formalisation: Tierney & Kadane (1986)	—
Typ	Approximate inference algorithm	Analytical posterior approximation	Posterior sampling algorithm
Ursprungskälla	Minka, T. P. (2001). Expectation propagation for approximate Bayesian inference. In Proceedings of the Seventeenth Conference on Uncertainty in Artificial Intelligence (UAI-01), pp. 362–369. Morgan Kaufmann.	Tierney, L. & Kadane, J. B. (1986). Accurate approximations for posterior moments and marginal densities. Journal of the American Statistical Association, 81(393), 82–86.	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
Alias	EP, expectation propagation, EP algorithm, assumed-density filtering generalisation	Laplace's method, saddle-point approximation (Bayesian), second-order Gaussian approximation, LA	markov chain monte carlo, MCMC sampling, MCMC (Markov Zinciri Monte Carlo)
Närliggande	3	3	3
Sammanfattning	Expectation Propagation (EP) is a deterministic message-passing algorithm for approximate posterior inference in Bayesian models, introduced by Thomas P. Minka at UAI 2001. It iteratively refines a set of local approximate factors — each drawn from the exponential family — so that their product closely matches the true intractable posterior, achieving higher accuracy than mean-field variational inference on many probabilistic machine learning tasks.	The Laplace approximation is a classical analytic technique that replaces an intractable posterior distribution with a multivariate Gaussian centred at the posterior mode, using the curvature of the log-posterior at that mode to set the covariance. Formalised for Bayesian statistics by Tierney and Kadane (1986) in their landmark Journal of the American Statistical Association paper, it provides a fast, deterministic alternative to Markov chain Monte Carlo and forms the mathematical core of Integrated Nested Laplace Approximations (INLA).	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.