  This paper presents a new modeling strategy for joint unsupervised analysis
of multiple high-throughput biological studies. As in Multi-study Factor
Analysis, our goals are to identify both common factors shared across studies
and study-specific factors. Our approach is motivated by the growing body of
high-throughput studies in biomedical research, as exemplified by the
comprehensive set of expression data on breast tumors considered in our case
study. To handle high-dimensional studies, we extend Multi-study Factor
Analysis using a Bayesian approach that imposes sparsity. Specifically, we
generalize the sparse Bayesian infinite factor model to multiple studies. We
also devise novel solutions for the identification of the loading matrices: we
recover the loading matrices of interest ex-post, by adapting the orthogonal
Procrustes approach. Computationally, we propose an efficient and fast Gibbs
sampling approach. Through an extensive simulation analysis, we show that the
proposed approach performs very well in a range of different scenarios, and
outperforms standard Factor analysis in all the scenarios identifying
replicable signal in unsupervised genomic applications. The results of our
analysis of breast cancer gene expression across seven studies identified
replicable gene patterns, clearly related to well-known breast cancer pathways.
An R package is implemented and available on GitHub.
