Brain-computer interfaces (BCIs) use brain signals to convey a user's intent. Some BCI approaches begin by decoding kinematic parameters of movements from brain signals, and then proceed to using these signals, in absence of movements, to allow a user to control an output. Recent results have shown that electrocorticographic (ECoG) recordings from the surface of the brain in humans can give information about kinematic parameters (eg{} hand velocity or finger flexion). The decoding approaches in these studies usually employed classical classification/regression algorithms that derive a linear mapping between brain signals and outputs. However, they typically only incorporate little prior information about the target movement parameter. In this paper, we incorporate prior knowledge using a Bayesian decoding method, and use it to decode finger flexion from ECoG signals. Specifically, we exploit the anatomic constraints and dynamic constraints that govern finger flexion and incorporate these constraints in the construction, structure, and the probabilistic functions of the prior model of a switched non-parametric dynamic system (SNDS). Given a measurement model resulting from a traditional linear regression method, we decoded finger flexion using posterior estimation that combined the prior and measurement models. Our results show that the application of the Bayesian decoding model, which incorporates prior knowledge, improves decoding performance compared to the application of a linear regression model, which does not incorporate prior knowledge. Thus, the results presented in this paper may ultimately lead to neurally controlled hand prostheses with full fine-grained finger articulation.