方法对比

	贝叶斯多重对应分析 (BMCA)	贝叶斯聚类分析
领域	统计学	统计学
方法族	Latent structure	Latent structure
起源年份	2000s–2010s	1998–2002
提出者	Extension of MCA (Benzecri, 1973) with Bayesian inference	Fraley & Raftery (model-based); Dirichlet process formulations by Ferguson (1973) and Antoniak (1974)
类型	Bayesian dimension reduction for categorical data	Probabilistic / model-based clustering
开创性文献	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.
别名	Bayesian MCA, BMCA, Bayesian multiway correspondence analysis, Bayesian categorical dimension reduction	BCA, Bayesian clustering, probabilistic cluster analysis, Bayesian model-based clustering
相关	5	6
摘要	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.