MOTIVATION: Pseudotime estimation from single-cell gene expression data allows the recovery of temporal information from otherwise static profiles of individual cells. Conventional pseudotime inference methods emphasize an unsupervised transcriptome-wide approach and use retrospective analysis to evaluate the behaviour of individual genes. However, the resulting trajectories can only be understood in terms of abstract geometric structures and not in terms of interpretable models of gene behaviour. RESULTS: Here we introduce an orthogonal Bayesian approach termed 'Ouija' that learns pseudotimes from a small set of marker genes that might ordinarily be used to retrospectively confirm the accuracy of unsupervised pseudotime algorithms. Crucially, we model these genes in terms of switch-like or transient behaviour along the trajectory, allowing us to understand why the pseudotimes have been inferred and learn informative parameters about the behaviour of each gene. Since each gene is associated with a switch or peak time the genes are effectively ordered along with the cells, allowing each part of the trajectory to be understood in terms of the behaviour of certain genes. We demonstrate that this small panel of marker genes can recover pseudotimes that are consistent with those obtained using the entire transcriptome. Furthermore, we show that our method can detect differences in the regulation timings between two genes and identify 'metastable' states-discrete cell types along the continuous trajectories-that recapitulate known cell types. AVAILABILITY AND IMPLEMENTATION: An open source implementation is available as an R package at http://www.github.com/kieranrcampbell/ouija and as a Python/TensorFlow package at http://www.github.com/kieranrcampbell/ouijaflow. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.