A new preprint “An importance sampling approach for reliable and efficient inference in Bayesian ordinary differential equation models” with @jtimonen, @Niko, @bbbales2, Harri Lähdesmäki
We show how to get an order of magnitude faster inference with ODEs and MCMC by starting with less strict tolerances, and by using Pareto smoothed importance sampling for diagnosing and improving the posterior inference to match results with stricter tolerances.
We forgot to cite (but now added) Hastings (1970) who discusses using IS to improve approximate but faster MCMC. Our contribution is the detailed analysis when using the approach with various ODE solvers and using also Pareto-\hat{k} diagnostic to check whether IS improvement is good enough.
The ODE model sampling was done with Stan, and the odemodeling R package for making all this easy is available at GitHub - jtimonen/odemodeling: R-package for building and fitting Bayesian ODE models in Stan. @jtimonen did awesome job with the paper and the package!
The approach can also be used for other than ODE models with numerical methods with tunable tolerances.