We propose a generic Bayesian mixed-effects model to estimate the temporal progression of a biological phenomenon from observations obtained at multiple time points for a group of individuals. The progression is modeled by continuous trajectories in the space of measurements. The group-average trajectory is defined by the fixed effects of the model. At the individuals level, the trajectories of progression result from spatio-temporal transformations of the average trajectory. These transformations, defined by the subject-specific random effects, allow to quantify the changes in direction and pace at which the trajectories are followed. The framework of Riemannian geometry allows the model to be used with any kind of measurements with smooth constraints. A stochastic version of the Expectation-Maximization algorithm is used to produce produce maximum a posteriori estimates of the parameters. Experimental results illustrate the ability of the model to be used with measurements of varying nature and complexity. In particular, we estimated a normative scenario of the impairment of cognitive functions during the course of Alzheimer's disease. We also show that the proposed model can be used to estimate a scenario of evolution of symmetric positive definite matrices.