方法对比

	贝叶斯主成分分析 (BPCA)	贝叶斯探索性因子分析 (Bayesian Exploratory Factor Analysis, BEFA)
领域	统计学	心理测量学
方法族	Latent structure	Latent structure
起源年份	1999	2004 (Bayesian formulation); factor analysis roots: 1904
提出者	Christopher M. Bishop	Lopes & West (seminal Bayesian treatment); roots in classical factor analysis (Spearman, 1904)
类型	Bayesian latent variable / dimension reduction	Probabilistic latent variable model
开创性文献	Bishop, C. M. (1999). Bayesian PCA. In M. S. Kearns, S. A. Solla & D. A. Cohn (Eds.), Advances in Neural Information Processing Systems 11 (pp. 382–388). MIT Press.	Lopes, H. F. & West, M. (2004). Bayesian model assessment in factor analysis. Statistica Sinica, 14(1), 41–67.
别名	BPCA, Bayesian PCA, probabilistic PCA with Bayesian inference, variational Bayesian PCA	Bayesian factor analysis, BEFA, Bayesian common factor model, probabilistic factor analysis
相关	2	4
摘要	Bayesian principal component analysis embeds probabilistic PCA within a Bayesian framework, placing priors over the loading matrix so that irrelevant components are automatically pruned. It handles missing data naturally and provides principled uncertainty estimates for both the latent scores and the dimensionality of the representation.	Bayesian exploratory factor analysis applies a full probabilistic framework to the common factor model. By placing prior distributions over factor loadings and unique variances, it yields posterior distributions rather than point estimates, quantifies uncertainty around every loading, and can treat the number of factors as an unknown to be inferred from data.