قارن الطرق

	نمذجة المزيج البايزي	تحليل الفئات الكامنة البايزي (BLCA)
المجال	الإحصاء	الإحصاء
العائلة	Latent structure	Latent structure
سنة النشأة	1997 (Richardson & Green Bayesian formulation)	1990s–2000s
صاحب الطريقة	Richardson & Green (seminal Bayesian treatment, 1997); broader Bayesian mixture roots trace to Dempster, Laird & Rubin (EM, 1977) and Titterington, Smith & Makov (1985)	Lazarsfeld (classical LCA); Bayesian formulation developed through Cheeseman & Stutz (1996) and Dunson & Xing (2009)
النوع	Latent-class / model-based clustering	Bayesian latent variable / finite mixture model
المصدر التأسيسي	Fruhwirth-Schnatter, S., Celeux, G. & Robert, C. P. (Eds.) (2019). Handbook of Mixture Analysis. CRC Press / Chapman & Hall. ISBN: 9780367733995	Dunson, D. B. & Xing, C. (2009). Nonparametric Bayes modeling of multivariate categorical data. Journal of the American Statistical Association, 104(487), 1042–1051.
الأسماء البديلة	Bayesian mixture model, BMM, Bayesian model-based clustering, Bayesian finite mixture	Bayesian LCA, BLCA, Bayesian mixture of multinomials, Bayesian finite mixture model
ذات صلة	4	6
الملخص	Bayesian mixture modeling represents the population as a weighted sum of K component distributions and estimates all unknowns — mixing weights, component parameters, and even the number of components — through posterior inference. It extends classical mixture analysis by placing priors on every parameter and quantifying uncertainty over latent group assignments rather than treating them as fixed.	Bayesian latent class analysis extends classical LCA by placing prior distributions on all model parameters and using posterior inference — typically via MCMC — to classify individuals into unobserved categorical groups, quantify uncertainty around class membership, and select the number of classes in a principled, probabilistic way.