By dynamical coupling of data with known models, we determine underlying parameters and unmeasured state variables for a variety of systems, including Lorenz, Colpitts, and Hodgkin-Huxley neurons. The dynamic coupling is mediated by use of a cost function, which is minimized by optimization software (SNOPT, IPOPT) to achieve the desired synchronization. Considering measurement and model noise, we discuss the same problem where we introduced an 'action' in order to estimate states and parameters. This action is used along with Markov Chain Monte Carlo methods in order to sample from a probability distribution.