Robust posterior inference when statistically emulating forward simulations
This work addresses the need for controlled approximations in scientific simulations, particularly in cosmology, but is incremental as it reviews and updates a previously published method.
The paper tackles the problem of safely approximating slow forward models in scientific analyses by updating a method to train an emulator while estimating posterior probabilities with MCMC and propagating emulation errors into parameter posterior errors. It demonstrates application to the ΛCDM cosmology model for quick posterior estimation and robustness assessment.
Scientific analyses often rely on slow, but accurate forward models for observable data conditioned on known model parameters. While various emulation schemes exist to approximate these slow calculations, these approaches are only safe if the approximations are well understood and controlled. This workshop submission reviews and updates a previously published method, which has been used in cosmological simulations, to (1) train an emulator while simultaneously estimating posterior probabilities with MCMC and (2) explicitly propagate the emulation error into errors on the posterior probabilities for model parameters. We demonstrate how these techniques can be applied to quickly estimate posterior distributions for parameters of the $Λ$CDM cosmology model, while also gauging the robustness of the emulator approximation.