For teaching, I’m looking for some interesting (practically) unidentifiable models which, ideally, are quite simple. I have a couple of examples that I use (the Lotka-Volterra ODE model with Gaussian noise sampled sparsely, for example), but I’m sure there are better and simpler ones out there.

Specifically, I’m looking for a model + data where:

- The model is relatively simple to explain
- Ideally, the model has relatively few parameters, so can be compactly written down
- Generating simulated data from the model is straightforward so that the class could do this as part of the exercise to show the system is unidentified
- The reason for the unidentification is non-trivial. So, for example, it’s not (say) a regression model where two parameters appear in the likelihood as a product

I’m looking for an example that’d be good for an audience of early career researchers who are just beginning in Bayesian inference.

Does anyone have a favourite example here?