This letter considers the model discrimination problem for switched nonlinear systems, where the switching sequence is constrained by metric/signal temporal logic specifications. Specifically, we propose an optimization-based algorithm for analyzing the detectability of the models from noisy, finite data as well as a model discrimination algorithm for nonlinear parameter-varying systems to rule out models that are inconsistent with observations at run time, by checking the feasibility of corresponding mixed-integer linear programs. Moreover, we apply the algorithms to nonlinear systems subject to ( m, k)-firm data losses and explicitly provide the integer constraints corresponding to the ( m, k)-firm constraints for lossy/missing data. Finally, we demonstrate the effectiveness of our approaches using several illustrative examples on fault detection, swarm consensus and intent identification problems.