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	Analisi delle Componenti Principali Bayesiana (BPCA)	Analisi Fattoriale Esplorativa Bayesiana (BEFA)
Campo	Statistica	Psicometria
Famiglia	Latent structure	Latent structure
Anno di origine	1999	2004 (Bayesian formulation); factor analysis roots: 1904
Ideatore	Christopher M. Bishop	Lopes & West (seminal Bayesian treatment); roots in classical factor analysis (Spearman, 1904)
Tipo	Bayesian latent variable / dimension reduction	Probabilistic latent variable model
Fonte seminale	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.
Alias	BPCA, Bayesian PCA, probabilistic PCA with Bayesian inference, variational Bayesian PCA	Bayesian factor analysis, BEFA, Bayesian common factor model, probabilistic factor analysis
Correlati	2	4
Sintesi	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.