Cosmological parameter estimations can require many thousands of time-consuming evaluations of the likelihood function. We show that computed likelihoods can be used to train an emulator that accurately predicts likelihoods for later points in the MCMC analyses and roll the uncertainty in the prediction into the parameter estimates themselves. Speed-ups for Planck parameter estimates were on the order of 60 to 100x.
Abstract
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 ΛCDM cosmology model, while also gauging the robustness of the emulator approximation.
- Aslanyan, Easther, Musoke and Price
- Robust posterior inference when statistically emulating forward simulations
- Workshop paper at ICLR 2020: Fundamental Science in the Era of AI, ArXiv:2004.11929
- Code and git repository
Posterior distributions of the baryon density Ωbh2 with (solid blue) and without (dashed red) emulation with different samplers.