Coherent states can be looked at as probability amplitudes over symplectic manifolds. From the point of view of operational physics, classical motions in \({\mathbb {R}}^{2m}\) are subject of uncertainties in the measuring devices and the presence of noise. In the case of Hamiltonian systems, this leads us to consider orbits in the neighborhood of the solutions of the equations of motion. These linearized flows are determined by symplectic matrices. The Koopman representation is natural for describing dynamical systems under the influence of random factors. Koopman states are presentented as coherent states bundles over phase space. On the other hand, the set of probability distributions, a statistical manifold, can be parametrized by positive Hermitian matrices for the same situation. Coherent states, viewed as a time series of measurements appear as the common Hilbert space: a Gaussian field of random variables on Fock space.