Bayesian Gaussian process inference of RNA velocity as a probabilistic vector field on single-cell manifolds

RNA velocity analysis is widely used to infer cellular state transitions from single-cell transcriptomic data by estimating directional changes in gene expression. However, most existing methods provide deterministic velocity estimates despite substantial uncertainty arising from measurement noise, cell-state heterogeneity, and ambiguous transitions. In this paper, we introduce a Bayesian probabilistic framework that models RNA velocity as a continuous latent vector field over a low-dimensional representation of the cellular manifold. Using Gaussian Processes, our approach provides both velocity estimates and principled uncertainty quantification for each cell. The proposed framework incorporates neighborhood structure through (graph) manifold-aware kernels and facilitates scalable inference via sparse variational Gaussian processes. The proposed method yields smooth, globally consistent velocity fields along with calibrated uncertainty estimates that reflect local data density and dynamical ambiguity. Using benchmark single-cell datasets, including a pancreas dataset (approximately 3,700 cells), we demonstrate that uncertainty is stable, reproducible, and associated with biologically relevant regions such as transitional cell populations and lineage bifurcations. Furthermore, uncertainty increases under data subsampling, indicating robustness to limited data and sensitivity to out-of-distribution regions, thereby supporting reliable downstream analyses of cellular dynamics.