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I read Turchin's book, but what I didnt understand was how you could fit large-parameter models on such a small number of instances provided by history, w/o cherry-picking examples? What is the intuition?

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Because there aren't that few. I'd need to revisit some of it really, but even in the late 90s, when I was doing a custom PS major, we were using comparatively larger models for conflict analysis, like the "Correlates of War" project, which were coded well enough to do some rough but statistically useful runs with...as an undergraduate back then it felt like something really useful to compliment/challenge/reconcile with the more common case study format prevalent in the field.

https://correlatesofwar.org/ https://www.jessicamaves.com/forge.html https://www.csac.org.uk/dataset/ etc

Models with non-linear dynamics will often need 10^(12+) examples to fit.

You cannot, in practice, establish empirical adequacy of such models. (Making, imv, much of social "science" better regarded as semi-empirical speculation).

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