Methoden vergleichen

	Bayesian Principal Component Analysis (BPCA)	Bayesian explorative Faktoranalyse (BEFA)
Fachgebiet	Statistik	Psychometrie
Familie	Latent structure	Latent structure
Entstehungsjahr	1999	2004 (Bayesian formulation); factor analysis roots: 1904
Urheber	Christopher M. Bishop	Lopes & West (seminal Bayesian treatment); roots in classical factor analysis (Spearman, 1904)
Typ	Bayesian latent variable / dimension reduction	Probabilistic latent variable model
Wegweisende Quelle	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.
Aliasnamen	BPCA, Bayesian PCA, probabilistic PCA with Bayesian inference, variational Bayesian PCA	Bayesian factor analysis, BEFA, Bayesian common factor model, probabilistic factor analysis
Verwandt	2	4
Zusammenfassung	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.