قارن الطرق

	سلاسل ماركوف مونت كارلو (MCMC)	نموذج التأثيرات المختلطة
المجال	بايزي	الإحصاء
العائلة	Bayesian methods	Regression model
سنة النشأة	—	1982
صاحب الطريقة	—	Laird & Ware
النوع	Posterior sampling algorithm	Mixed effects regression
المصدر التأسيسي	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	Laird, N. M., & Ware, J. H. (1982). Random-effects models for longitudinal data. Biometrics, 38(4), 963–974.
الأسماء البديلة	markov chain monte carlo, MCMC sampling, MCMC (Markov Zinciri Monte Carlo)	LME, LMM, mixed model, random effects model
ذات صلة	3	4
الملخص	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.	A mixed effects model (or linear mixed model) extends ordinary regression by including both fixed effects — population-level parameters shared by all observations — and random effects that capture subject-, group-, or cluster-level variability. It is the standard tool for repeated-measures, longitudinal, and multilevel data where observations within the same unit are correlated.