Methoden vergleichen

	Bayesian Multiple Correspondence Analysis (BMCA)	Bayesian Clusteranalyse
Fachgebiet	Statistik	Statistik
Familie	Latent structure	Latent structure
Entstehungsjahr	2000s–2010s	1998–2002
Urheber	Extension of MCA (Benzecri, 1973) with Bayesian inference	Fraley & Raftery (model-based); Dirichlet process formulations by Ferguson (1973) and Antoniak (1974)
Typ	Bayesian dimension reduction for categorical data	Probabilistic / model-based clustering
Wegweisende Quelle	Greenacre, M. & Blasius, J. (Eds.) (2006). Multiple Correspondence Analysis and Related Methods. Chapman & Hall/CRC. ISBN: 978-1584886280	Fraley, C. & Raftery, A. E. (2002). Model-based clustering, discriminant analysis, and density estimation. Journal of the American Statistical Association, 97(458), 611–631.
Aliasnamen	Bayesian MCA, BMCA, Bayesian multiway correspondence analysis, Bayesian categorical dimension reduction	BCA, Bayesian clustering, probabilistic cluster analysis, Bayesian model-based clustering
Verwandt	5	6
Zusammenfassung	Bayesian Multiple Correspondence Analysis extends classical MCA by embedding the geometric decomposition of categorical data tables within a Bayesian probabilistic framework, enabling principled uncertainty quantification around category coordinates, dimension selection via marginal likelihood, and incorporation of prior knowledge about variable relationships.	Bayesian cluster analysis assigns observations to latent groups by combining a probabilistic model of within-cluster data with prior beliefs about cluster parameters and the number of clusters. It yields posterior probabilities of cluster membership and principled uncertainty estimates, making it more transparent than classical distance-based clustering algorithms.