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Abstract Disease etiology may be better understood through the study of gene expression in four dimensional (4D) experiments that consist of measurements on multiple individuals, genes, tissues and under multiple conditions or through time. We have developed a sparse Bayesian four dimensional tensor decomposition method aimed at uncovering latent components or gene networks that could be linked to genetic variation. We used a Variational Bayes algorithm to fit the model which provides fast and accurate analysis. In this brief note we illustrate the utility of the method using simulated datasets, and show that when 4D data is available our method shows improved performance in estimating the true structure in the dataset, when compared to using a 3D method on a single slice of the 4D dataset. We also compare the results of the 4D method to that of the 3D method on a suitable unfolding of the dataset, demonstrating that similar performance is observed in this case, while the 4D method accurately recovers the additional structure in the data. We provide software that implements the method in R.

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