Reconstructing Probability Distributions with Gaussian Processes. (arXiv:1905.09299v1 [astro-ph.CO])
<a href="http://arxiv.org/find/astro-ph/1/au:+McClintock_T/0/1/0/all/0/1">Thomas McClintock</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Rozo_E/0/1/0/all/0/1">Eduardo Rozo</a>
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.
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.
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