Simulation-based inference for cultural evolution: a tutorial with baby name data

Cultural evolutionary models are usually easy to simulate but difficult to fit, because most have no tractable likelihood. Simulation-based inference (SBI) addresses this by treating the simulator itself as the likelihood, and now ranges from rejection-based approximate Bayesian computation (ABC) to amortized neural posterior estimation (NPE). Knowing which to use is hard, partly because they are rarely compared on the same model and data. In this tutorial I fit a Wright-Fisher-style model of baby name popularity to uncensored female naming records from South Australia (1944-2017, with inference on 1981-2017), comparing rejection ABC, ABC with random forests, and NPE with BayesFlow on one shared set of 10,000 simulations. The model includes frequency dependence (β), an age-dependent bias (α), and random variation (γ). Recovery varies widely across parameters and methods, from r = 0.96-1.00 for β to r = 0.39-0.97 for γ, and these differences track what each estimator does with the summary statistics it is given and, for γ, how much of the signal those statistics retain. I use the comparison to work through what makes a parameter identifiable, the diagnostics that indicate whether a posterior can be trusted, and common failure modes. All code and data are provided.