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We present a probabilistic model for a document corpus that combines many of the desirable features of previous models. The model is called "GaP" for Gamma-Poisson, the distributions of the first and last random variable. GaP is a factor model, that is it gives an approximate factorization of the document-term matrix into a product of matrices Λ and X. These factors have strictly non-negative terms. GaP is a generative probabilistic model that assigns finite probabilities to documents in a corpus. It can be computed with an efficient and simple EM recurrence. For a suitable choice of parameters, the GaP factorization maximizes independence between the factors. So it can be used as an independent-component algorithm adapted to document data. The form of the GaP model is empirically as well as analytically motivated. It gives very accurate results as a probabilistic model (measured via perplexity) and as a retrieval model. The GaP model projects documents and terms into a low-dimensional space of "themes," and models texts as "passages" of terms on the same theme.