We develop new techniques for time series classification based on hierarchical Bayesian generative models (called mixed-effect models) and the Fisher kernel derived from them. A key advantage of the new formulation is that one can compute the Fisher information matrix despite varying sequence lengths and sampling times. We therefore can avoid the ad hoc replacement of Fisher information matrix with the identity matrix commonly used in literature, which destroys the geometrical grounding of the kernel construction. In contrast, our construction retains the proper geometric structure resulting in a kernel that is properly invariant under change of coordinates in the model parameter space. Experiments on detecting cognitive decline show that classifiers based on the proposed kernel out-perform those based on generative models and other feature extraction routines.