Reconstructing Probability Distributions with Gaussian Processes

Abstract

Modern cosmological analyses constrain physical parameters using Markov Chain Monte Carlo (MCMC) or similar sampling techniques. Oftentimes, these techniques are computationally expensive to run and require up to thousands of CPU hours to complete. Here we present a method for reconstructing the log-probability distributions of completed experiments from an existing MCMC chain (or any set of posterior samples). The reconstruction is performed using Gaussian process regression for interpolating the log-probability. This allows for easy resampling, importance sampling, marginalization, testing different samplers, investigating chain convergence, and other operations. As an example use-case, we reconstruct the posterior distribution of the most recent Planck 2018 analysis. We then resample the posterior, and generate a new MCMC chain with forty times as many points in only thirty minutes. Our likelihood reconstruction tool can be found online at https://github.com/tmcclintock/AReconstructionTool.