# Reconstructing Probability Distributions with Gaussian Processes

## TL;DR

This paper introduces a Gaussian process-based method to reconstruct and resample probability distributions from existing MCMC samples, significantly reducing computational costs for cosmological data analysis.

## Contribution

The authors present a novel Gaussian process regression approach to reconstruct log-probability distributions from MCMC samples, enabling efficient resampling and analysis.

## Key findings

- Reconstructed the Planck 2018 posterior distribution.
- Generated a new MCMC chain with forty times more points in thirty minutes.
- Demonstrated the method's utility for importance sampling and convergence testing.

## 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.