Bayesian prior impact assessment for dynamical systems described by ordinary differential equations

In this study we extend the use of the Wasserstein Impact Measure (WIM) to the problem of assessing prior impact in Bayesian models governed by systems of ordinary differential equations (ODEs) with moderate (5 to 10) parametric dimension. First, we utilise algorithms from computational optimal transport to compute the WIM in moderate parametric dimensions. Second, we propose a new prior scaled Wasserstein Impact Measure (sWIM) measure which gives a relative sense of distance, easing with interpretation of the WIM for understanding the impact of the prior on the resulting in- ference. We show numerical computation and interpretation of the WIM and sWIM for a Lotka-Volterra predator-prey model calibrated against the Hudson Bay Company dataset and a compartment epidemiological model calibrated against first-wave COVID-19 data from Luxembourg.