I have a deterministic ODE model that I want to fit to time series data. I’m interested in performing parameter inference using Stan, but without relying on the usual likelihood-based methods. Are there any tutorials or example codes demonstrating how to do this, perhaps for a simple SI or SIR model, using Approximate Bayesian Computation (ABC) or a similar approach?
Welcome to the Stan community!
There are a number of blog posts/case studies that cover ODE models in Stan, some examples:
The last of which describes a SIR model. I can’t speak to the ABC side of it, but these may be reasonable places to start.
Is there a specific reasons why you don’t want to use a likelihood-based inference?
Epidemiological models are usually prototypical examples of having data compatible with full likelihoods, which are expected to provide the best results.
If you have what you consider informative summaries, I guess in principle it should be straightforward to compute them from an ODE simulation, but I think Stan expects the log-posterior to follow a log-prior plus log-likelihood structure, so I’m not sure how the summaries would be incorporated there, so it may be possible but cumbersome to implement it.