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. In the paper, 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.