Table 1
Three type of time-series data over vector spaces, and papers showing how to fit those types of time series with a Markov process. (Current as of 2023.)
| TIME SERIES TYPE | ALGORITHM |
|---|---|
| Homogeneous and/or very little data | (Pavliotis 2016) |
| Inhomogeneous, missing fields in data | (Yildiz et al. 2018) |
| Inhomogeneous, no missing fields in data | (Kidger et al. 2020, Li et al. 2020) |
Figure 1
The mean value of PC2 as a function of PC1, where the mean and error bars are calculated using a sliding window with a width of 1.0 in PC1-space. The top curve is identical to that in (Shin et al. 2020). The middle plot uses the new Seshat Equinox dataset, but the new NGAs added to Equinox have been removed. The bottom plot uses the new dataset and utilizes all Equinox NGAs. The key difference between the original datasest and the Equinox dataset is that the latter dataset uses one fewer CCs, collapsing the two original information processes CCs into a single CC. These figures can be reproduced using the code in the publication github repository (see supplement).
Figure 2
Histogram of PC1 values for all polity-time pairs. The top curve is identical to that in (Shin et al. 2020). The middle plot uses the new Seshat Equinox dataset, but the new NGAs added to Equinox have been removed. The bottom plot uses the new dataset and utilizes all Equinox NGAs. The key difference between the original datasest and the Equinox dataset is that the latter dataset uses one fewer CCs, collapsing the two original information processes CCs into a single CC. These figures can be reproduced using the code in the publication github repository (see supplement).
Figure 3
The two axes are PC1 and PC2 of the (original) Seshat dataset, respectively. The red dots are the elements of that dataset. Since those elements of the dataset are time-stamped, one can find the Langevin SDE that has highest posterior probability conditioned on that dataset. The black arrows are the mean velocity vectors of that Langevin equation at the associated PC1-PC2 positions (i.e., they are values of the drift vector field of that SDE evaluated on a grid). Finally, the blue lines are counterfactual, sample trajectories of that SDE.