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It has been hypothesized that during a motion task the central nervous system controls the skeletal muscles partitioning them into synergetic groups, hence effectively reducing the dimensionality of the control problem. The identification of muscle groups that are co-activated remains an open problem: its solution could have important implications in the design of training or rehabilitation protocols. In this article, we combine Bayesian inverse problem techniques and data science algorithms to identify muscle synergies in human motion from the motion tracker time series of positions of fiducial markers on the body during the task. The inverse problem of estimating the muscle activation patterns from the motion tracking data is cast in the Bayesian framework, and the posterior distribution of muscle activations is explored using Myobolica, a Gibbs-sampler-based Markov chain Monte Carlo sampler. A low-rank approximation of the muscle activation patterns is then obtained via a sparsity promoting Bayesian non-negative matrix factorization of the sample mean, where the sparse coefficient vectors correspond to groups of muscles that show co-activation over the sample. This article is part of the theme issue ‘Frontiers of applied inverse problems in science and engineering’.