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 logprobability distributions of completed experiments from an existing chain (or any set of posterior samples). Here, the reconstruction is performed using Gaussian process regression for interpolating the logprobability. 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 chain with 40 times as many points in only 30 min. Our likelihood reconstruction tool is made publicly available online.
 Authors:

 Brookhaven National Lab. (BNL), Upton, NY (United States). Physics Dept.
 Univ. of Arizona, Tuscon, AZ (United States). Dept. of Physics
 Publication Date:
 Research Org.:
 Brookhaven National Lab. (BNL), Upton, NY (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC), High Energy Physics (HEP)
 OSTI Identifier:
 1573465
 Report Number(s):
 BNL2123142019JAAM
Journal ID: ISSN 00358711; TRN: US2001369
 Grant/Contract Number:
 SC0012704
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Monthly Notices of the Royal Astronomical Society
 Additional Journal Information:
 Journal Volume: 489; Journal Issue: 3; Journal ID: ISSN 00358711
 Publisher:
 Royal Astronomical Society
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; methods; data analysis; statistical
Citation Formats
McClintock, Thomas, and Rozo, Eduardo. Reconstructing probability distributions with Gaussian processes. United States: N. p., 2019.
Web. doi:10.1093/mnras/stz2426.
McClintock, Thomas, & Rozo, Eduardo. Reconstructing probability distributions with Gaussian processes. United States. doi:10.1093/mnras/stz2426.
McClintock, Thomas, and Rozo, Eduardo. Mon .
"Reconstructing probability distributions with Gaussian processes". United States. doi:10.1093/mnras/stz2426. https://www.osti.gov/servlets/purl/1573465.
@article{osti_1573465,
title = {Reconstructing probability distributions with Gaussian processes},
author = {McClintock, Thomas and Rozo, Eduardo},
abstractNote = {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 logprobability distributions of completed experiments from an existing chain (or any set of posterior samples). Here, the reconstruction is performed using Gaussian process regression for interpolating the logprobability. 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 chain with 40 times as many points in only 30 min. Our likelihood reconstruction tool is made publicly available online.},
doi = {10.1093/mnras/stz2426},
journal = {Monthly Notices of the Royal Astronomical Society},
number = 3,
volume = 489,
place = {United States},
year = {2019},
month = {9}
}
Web of Science
Works referenced in this record:
ChainConsumer
journal, August 2016
 Hinton, Samuel
 The Journal of Open Source Software, Vol. 1, Issue 4
Dark Energy Survey Year 1 Results: A Precise H0 Estimate from DES Y1, BAO, and D/H Data
journal, July 2018
 Abbott, T. M. C.; Abdalla, F. B.; Annis, J.
 Monthly Notices of the Royal Astronomical Society, Vol. 480, Issue 3
emcee : The MCMC Hammer
journal, March 2013
 ForemanMackey, Daniel; Hogg, David W.; Lang, Dustin
 Publications of the Astronomical Society of the Pacific, Vol. 125, Issue 925
The MiraTitan Universe. II. Matter Power Spectrum Emulation
journal, September 2017
 Lawrence, Earl; Heitmann, Katrin; Kwan, Juliana
 The Astrophysical Journal, Vol. 847, Issue 1
Hunting high and low: disentangling primordial and latetime nonGaussianity with cosmic densities in spheres
journal, October 2017
 Uhlemann, C.; Pajer, E.; Pichon, C.
 Monthly Notices of the Royal Astronomical Society, Vol. 474, Issue 3
The clustering of galaxies in the completed SDSSIII Baryon Oscillation Spectroscopic Survey: cosmological analysis of the DR12 galaxy sample
journal, March 2017
 Alam, Shadab; Ata, Metin; Bailey, Stephen
 Monthly Notices of the Royal Astronomical Society, Vol. 470, Issue 3
Fast Direct Methods for Gaussian Processes
journal, February 2016
 Ambikasaran, Sivaram; ForemanMackey, Daniel; Greengard, Leslie
 IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 38, Issue 2
Conservative constraints on early cosmology with M ONTE P YTHON
journal, February 2013
 Audren, Benjamin; Lesgourgues, Julien; Benabed, Karim
 Journal of Cosmology and Astroparticle Physics, Vol. 2013, Issue 02
CosmoSIS: Modular cosmological parameter estimation
journal, September 2015
 Zuntz, J.; Paterno, M.; Jennings, E.
 Astronomy and Computing, Vol. 12
Gaussian Processes for Machine Learning
book, January 2005
 Rasmussen, Carl Edward; Williams, Christopher K. I.
 The MIT Press
The Coyote Universe. ii. Cosmological Models and Precision Emulation of the Nonlinear Matter Power Spectrum
journal, October 2009
 Heitmann, Katrin; Higdon, David; White, Martin
 The Astrophysical Journal, Vol. 705, Issue 1
Dark Energy Survey Year 1 results: Methodology and projections for joint analysis of galaxy clustering, galaxy lensing, and CMB lensing twopoint functions
journal, January 2019
 Baxter, E. J.; Omori, Y.; Chang, C.
 Physical Review D, Vol. 99, Issue 2
Matplotlib: A 2D Graphics Environment
journal, January 2007
 Hunter, John D.
 Computing in Science & Engineering, Vol. 9, Issue 3
Cosmological parameters from CMB and other data: A Monte Carlo approach
journal, November 2002
 Lewis, Antony; Bridle, Sarah
 Physical Review D, Vol. 66, Issue 10
Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant
journal, September 1998
 Riess, Adam G.; Filippenko, Alexei V.; Challis, Peter
 The Astronomical Journal, Vol. 116, Issue 3
The 6dF Galaxy Survey: baryon acoustic oscillations and the local Hubble constant: 6dFGS: BAOs and the local Hubble constant
journal, July 2011
 Beutler, Florian; Blake, Chris; Colless, Matthew
 Monthly Notices of the Royal Astronomical Society, Vol. 416, Issue 4
A Micromechanical Method for the Analysis of ThreeDimensional Smart Composites
journal, March 2018
 Ye, J. J.; Chu, Ch. Ch.; Wang, Y. K.
 Mechanics of Composite Materials, Vol. 54, Issue 1
Nuisance hardened data compression for fast likelihoodfree inference
journal, July 2019
 Alsing, Justin; Wandelt, Benjamin
 Monthly Notices of the Royal Astronomical Society, Vol. 488, Issue 4
Measurements of Ω and Λ from 42 High‐Redshift Supernovae
journal, June 1999
 Perlmutter, S.; Aldering, G.; Goldhaber, G.
 The Astrophysical Journal, Vol. 517, Issue 2
The NumPy Array: A Structure for Efficient Numerical Computation
journal, March 2011
 van der Walt, Stéfan; Colbert, S. Chris; Varoquaux, Gaël
 Computing in Science & Engineering, Vol. 13, Issue 2
The Aemulus Project. II. Emulating the Halo Mass Function
journal, February 2019
 McClintock, Thomas; Rozo, Eduardo; Becker, Matthew R.
 The Astrophysical Journal, Vol. 872, Issue 1
Cosmology from cosmic shear power spectra with Subaru Hyper SuprimeCam firstyear data
journal, March 2019
 Hikage, Chiaki; Oguri, Masamune; Hamana, Takashi
 Publications of the Astronomical Society of Japan, Vol. 71, Issue 2
Generalized Subset Designs in Analytical Chemistry
journal, May 2017
 Surowiec, Izabella; Vikström, Ludvig; Hector, Gustaf
 Analytical Chemistry, Vol. 89, Issue 12