Effective actions for statistical data assimilation

Data assimilation is a problem in estimating the fixed parameters and state of a model of an observed dynamical system as it receives inputs from measurements passing information to the model. Using methods developed in statistical physics, we present effective actions and equations of motion for the mean orbits associated with the temporal development of a dynamical model when it has errors, there is uncertainty in its initial state, and it receives information from noisy measurements. If there are statistical dependences among errors in the measurements they can be included in this approach.