Approximate Bayesian Computation for Panel Data with Signature Maximum Mean Discrepancies

Simulation models are becoming a staple tool across application domains from economics to biology. When such models are stochastic, evaluating their likelihood functions in a reasonable time is typically infeasible or even impossible. In these settings, simulation-based inference procedures are a convenient means to approximating conventional parameter calibration procedures. A popular example is approximate Bayesian computation, in which the observed data is compared to the simulation output at different parameter values through some distance function. While many such methods exist, few are compatible with panel data of various kinds, as might appear in medical settings, for example; many methods instead assume iid observations in both the simulated and observed data. We seek to address this gap through the use of signature maximum mean discrepancies as distance measures in approximate Bayesian computation. Through experiments with a dynamical model of functional brain networks, we demonstrate that such an approach can flexibly operate on panel data of various kinds, for example dynamic graph data arising from multiple patients/subjects in fMRI settings.