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Bayesian rank estimation with application to factor analysis. (English) Zbl 0813.62056
Summary: Rank estimation is a common sub-problem met in various fields exploiting matrix algebra. Estimation of the number of factors in factor analysis is of this type. Due to large noise contents in the analyzed matrix, standard procedures, like deterministic inspection of singular values, fail.
Here, a novel procedure is proposed. It is gained by straightforward application of Bayesian statistics to a carefully selected model which fits to the target area, namely, factor analysis of dynamic scintigraphic studies. The formal solution consists of an exactly feasible part and a maximum-likelihood type one. The latter is justified by large dimensions of the data matrices containing analyzed images. Properties of the procedure are illustrated on simulated and real data.

62H25 Factor analysis and principal components; correspondence analysis
62F15 Bayesian inference
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