Recovering \Lost" Information in the Presence of Noise:
Application to Population Ecology
A Hamiltonian approach to reconstruction of a trajectory and model of complex stochastic dynamics from noisy measurements is introduced. The method converges even when the entire trajectory components are unobservable and the conventional Monte Carlo technique fails. The method is applied to reconstruct the nonlinear models of predator-prey oscillations. We found that the projected (incomplete) character os measurements results in the likelihood distribution with two very different scales: it is strongly localized in the vicinity of a hyperplane in the joint parameters-trajectory space. This reflects the intrinsic tradeoff between the system parameters and hidden trajectory components.