Null Model
We build a Null Model that describes expected frequencies of dates in each decade under the assumption that all countries are presented equally. By comparing the observed frequencies with the expected baseline, we are able to detect significant focal points.
Our approach is essentially an urn model, with replacement and without duplication, based on the underlying Dirichlet-multinomial distribution. We illustrate the method with a toy example.
Illustration of the method on countries A and C. We plot a histogram of date counts for each country (green bins), and compare them with expected baselines (orange lines). The baselines are the average over four initial distributions, adjusted to match each country's total date count. Thus, the baselines are unique for every country and decade.
The initial distribution of toy data for hypothetical countries A-D. The dates are binned into decades, each cell colored according to the number of dates.
Finally, we convert the differences between the data and the baseline into z-scores.