1. Introduction#

In Superstats, a dynamic generative model is built from two pieces: a low-level observation model (e.g., a cognitive model such as the Diffusion Decision Model) that generates data at each time step, and a high-level transition model that describes how the model’s parameters evolve over time.

A typical amortized Bayesian workflow (Li et al., 2026) consists of the following steps:

  1. Define the observation model as a data simulator.

  2. Specify a joint prior, assigning a transition model to each parameter that should vary over time, and a standard prior to those that should not.

  3. Prior push-forward checks: Simulate from the generative model and ask whether the implied parameter trajectories and data are consistent with your domain knowledge. Adjust the priors and transition models until they are.

  4. Set up the amortized Bayesian workflow: specify a neural approximator consisting of a summary and inference network.

  5. Train the neural approximator on simulations from the generative model.

  6. Model verification: Check that the approximate posteriors are well calibrated (via simulation-based calibration) and that the model and design can answer your question at all (via parameter recovery and posterior contraction). If they cannot, return to steps 1–2 and revise.

  7. Fit empirical data for any number of datasets, at negligible cost.

  8. Evaluate the absolute model fit: Re-simulate data from the posterior and ask whether the model reproduces the patterns you care about. A model that misses them is not worth interpreting, no matter how well it did in step 6.

  9. Inspect the posteriors of the time-varying and time-invariant parameters.