I am working on the Bayesian infinitesimal jackknife, a technique for quickly approximating the frequentist covariance of Bayesian posterior expectations (see this blog post and this StanCon presentation). I’m looking for publicly available datasets and Stan models to try it out on, and wondered if the Stan forums have any suggestions for where to look.

The ideal applications are models and datsets with the following properties:

- A lot of exchangeable (conditionally independent) data points (ideally in the thousands of data points);
- A handful number of global parameters whose posterior means you’re interested in;
- A lot of parameters that you need to integrate out with MCMC (i.e., you couldn’t just get a good approximate fit with the Laplace approximation or with lme4);
- Some possibility of model misspecification.

All I need is the data, a model, and a description (in a paper or otherwise) of what the model is useful for. Rstanarm applications with random effects are also welcome.

I have already looked through the relevant datasets in the Stan examples; most are too small for the necessary asymptotics to kick in.