Graph-informed simulation-based inference for models of active matter

As we use more timesteps as summarising features, our posterior estimation becomes increasingly tighter around the true parameter values, as shown as blue curves in Figure 3. Here, we use only three timesteps, the initial structure of the system, the final structure of the system (as in orange), and halfway between these two timesteps. The overall increase in accuracy is relatively small compared to a single timestep but considerably tighter than using average velocity and MSD. In order to assess how well-calibrated our posteriors are, we compute the expected coverage, which quantifies the probability that a set of parameters will be included in the highest density region of probability of a posterior (for further details see Hermans et al. (2021)). This is shown in Figure 3.b. We observe that, while the estimated posterior calculated using summary statistics (average velocity and MSD) has larger spread of uncertainty, the expected coverage is above the diagonal implying that the posterior distributions are over-dispersed. On the other hand, the expected coverage for posteriors calculated using the interaction graph are lower, indicating they are under-dispersed. We see relatively little difference in the impact of the number of snapshots used. Future work will investigate how to improve the expected coverage of these graph-informed posteriors.