That makes sense, thanks! For fitting a single curve it behaved well, but once I tried fitting multiple curves simultaneously it got very bogged down, and the result was a bit weird. It could likely improve with more tuning on my part, but it seems like it wouldn’t really outperform NUTS. I still feel like evaluating the likelihood of each timeseries data point independently isn’t entirely appropriate, but I don’t know much about these things.
This is a slightly different implementation than I was referring to in my original post, but this paper presents an ABC-SMC approach to Bayesian design of a reaction network that I’m very interested in: https://www.pnas.org/content/108/37/15190