CombineHarvesterFlow: Joint Probe Analysis Made Easy with Normalizing Flows

Abstract

We show how to efficiently sample the joint posterior of two non-covariant experiments with a large set of nuisance parameters. Specifically, we train an ensemble of normalizing flows to learn the posterior distribution of both experiments. Once trained, we can use the flows to reweight $\mathcal{O} (10^9)$ samples from both measurements to compute the joint posterior in seconds -- saving up to $\mathcal{O}(1)$ ton of $\text{CO}_2$ per Monte Carlo run. Using this new technique we find joint constraints between the Dark Energy Survey $3 \times 2$ point measurement, South Pole Telescope and Planck CMB lensing and a BOSS direct fit full shape analyses, for the first time. We find $\Omega_{\rm m} = 0.32^{+0.01}_{-0.01}$ and $S_8 = 0.79 ^ {+0.01}_ {-0.01}$. We release a public package called {\tt CombineHarvesterFlow} (https://github.com/pltaylor16/CombineHarvesterFlow) which performs these calculations.