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Brain networks and the dynamics that unfold upon them are of vital importance at many scales of systems neuroscience. The parameterization of generative models from empirical data (inverse modelling) has become of great utility to theoretical understanding in this domain. However, it has become difficult to infer mechanisms of spontaneous neural activity with existing tools due to the adoption of simplifying model assumptions that appeal to steady-state approximations of neural dynamics. In this work we describe a framework employing Approximate Bayesian Computation (ABC) for the inversion of neural models that can be used to flexibly model any statistical feature of empirically recorded data without assuming any specific form of dynamics. Further, we demonstrate how Bayesian model comparison can be applied to ABC fitted models to facilitate the selection of competing dynamical hypotheses. This work provides a validation of this approach in the context of a Parkinsonian electrophysiology, using a set of multisite recordings from Parkinsonian rats to demonstrate convergence, consistency, and uniqueness of parameter estimation; face validity of the model comparison procedures; and its utility in answering biologically relevant problems. From the validation and example applications presented here we conclude that the proposed framework is likely to be of value to a wide range of researchers aiming to explain how brain dynamics emerge from neural circuits.