skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

This content will become publicly available on August 6, 2020

Title: Improved renormalization group computation of likelihood functions for cosmological data sets

Abstract

Evaluation of likelihood functions for cosmological large scale structure data sets (including CMB, galaxy redshift surveys, etc.) naturally involves marginalization, i.e., integration, over an unknown underlying random signal field. Recently, I showed how a renormalization group method can be used to carry out this integration efficiently by first integrating out the smallest scale structure, i.e., localized structure on the scale of differences between nearby data cells, then combining adjacent cells in a coarse graining step, then repeating this process over and over until all scales have been integrated. Here I extend the formulation in several ways in order to reduce the prefactor on the method's linear scaling with data set size. The key improvement is showing how to integrate out the difference between specific adjacent cells before summing them in the coarse graining step, compared to the original formulation in which small-scale fluctuations were integrated more generally. I suggest some other improvements in details of the scheme, including showing how to perform the integration around a maximum likelihood estimate for the underlying random field. In the end, an accurate likelihood computation for a million-cell Gaussian test data set runs in two minutes on my laptop, with room for further optimizationmore » and straightforward parallelization.« less

Authors:
ORCiD logo [1]
  1. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Publication Date:
Research Org.:
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)
OSTI Identifier:
1564070
Alternate Identifier(s):
OSTI ID: 1547984
Grant/Contract Number:  
AC02-05CH11231; AC02-05-CH11231
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review D
Additional Journal Information:
Journal Volume: 100; Journal Issue: 4; Journal ID: ISSN 2470-0010
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
79 ASTRONOMY AND ASTROPHYSICS

Citation Formats

McDonald, Patrick. Improved renormalization group computation of likelihood functions for cosmological data sets. United States: N. p., 2019. Web. doi:10.1103/physrevd.100.043511.
McDonald, Patrick. Improved renormalization group computation of likelihood functions for cosmological data sets. United States. doi:10.1103/physrevd.100.043511.
McDonald, Patrick. Tue . "Improved renormalization group computation of likelihood functions for cosmological data sets". United States. doi:10.1103/physrevd.100.043511.
@article{osti_1564070,
title = {Improved renormalization group computation of likelihood functions for cosmological data sets},
author = {McDonald, Patrick},
abstractNote = {Evaluation of likelihood functions for cosmological large scale structure data sets (including CMB, galaxy redshift surveys, etc.) naturally involves marginalization, i.e., integration, over an unknown underlying random signal field. Recently, I showed how a renormalization group method can be used to carry out this integration efficiently by first integrating out the smallest scale structure, i.e., localized structure on the scale of differences between nearby data cells, then combining adjacent cells in a coarse graining step, then repeating this process over and over until all scales have been integrated. Here I extend the formulation in several ways in order to reduce the prefactor on the method's linear scaling with data set size. The key improvement is showing how to integrate out the difference between specific adjacent cells before summing them in the coarse graining step, compared to the original formulation in which small-scale fluctuations were integrated more generally. I suggest some other improvements in details of the scheme, including showing how to perform the integration around a maximum likelihood estimate for the underlying random field. In the end, an accurate likelihood computation for a million-cell Gaussian test data set runs in two minutes on my laptop, with room for further optimization and straightforward parallelization.},
doi = {10.1103/physrevd.100.043511},
journal = {Physical Review D},
number = 4,
volume = 100,
place = {United States},
year = {2019},
month = {8}
}

Journal Article:
Free Publicly Available Full Text
This content will become publicly available on August 6, 2020
Publisher's Version of Record

Save / Share:

Works referenced in this record:

Primordial non-Gaussianity: Large-scale structure signature in the perturbative bias model
journal, December 2008


Structure formation from non-Gaussian initial conditions: Multivariate biasing, statistics, and comparison with N -body simulations
journal, March 2010


Signatures of primordial non-Gaussianities in the matter power-spectrum and bispectrum: the time-RG approach
journal, March 2010

  • Bartolo, Nicola; Almeida, Juan P. Beltrán; Matarrese, Sabino
  • Journal of Cosmology and Astroparticle Physics, Vol. 2010, Issue 03
  • DOI: 10.1088/1475-7516/2010/03/011

Scale-dependent bias from primordial non-Gaussianity with trispectrum: Halo bias with primordial trispectrum
journal, August 2011


Information field theory for cosmological perturbation reconstruction and nonlinear signal analysis
journal, November 2009


Scale-dependent galaxy bias from massive particles with spin during inflation
journal, January 2018

  • Dizgah, Azadeh Moradinezhad; Dvorkin, Cora
  • Journal of Cosmology and Astroparticle Physics, Vol. 2018, Issue 01
  • DOI: 10.1088/1475-7516/2018/01/010

Planck 2015 results : XI. CMB power spectra, likelihoods, and robustness of parameters
journal, September 2016


Bayesian reconstruction of the cosmological large-scale structure: methodology, inverse algorithms and numerical optimization
journal, September 2008


Renormalization group computation of likelihood functions for cosmological data sets
journal, February 2019


Large-scale structure perturbation theory without losing stream crossing
journal, January 2018


Information Theory for Fields
journal, January 2019


Towards optimal extraction of cosmological information from nonlinear data
journal, December 2017

  • Seljak, Uroš; Aslanyan, Grigor; Feng, Yu
  • Journal of Cosmology and Astroparticle Physics, Vol. 2017, Issue 12
  • DOI: 10.1088/1475-7516/2017/12/009

Global, exact cosmic microwave background data analysis using Gibbs sampling
journal, October 2004

  • Wandelt, Benjamin D.; Larson, David L.; Lakshminarayanan, Arun
  • Physical Review D, Vol. 70, Issue 8
  • DOI: 10.1103/PhysRevD.70.083511

The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: baryon acoustic oscillations in the Fourier space
journal, September 2016

  • Beutler, Florian; Seo, Hee-Jong; Ross, Ashley J.
  • Monthly Notices of the Royal Astronomical Society, Vol. 464, Issue 3
  • DOI: 10.1093/mnras/stw2373

Clustering of dark matter tracers: generalizing bias for the coming era of precision LSS
journal, August 2009


Estimating the power spectrum of the cosmic microwave background
journal, February 1998


Detection of gravitational lensing in the cosmic microwave background
journal, August 2007


How to estimate the 3D power spectrum of the Lyman-α forest
journal, January 2018

  • Font-Ribera, Andreu; McDonald, Patrick; Slosar, Anže
  • Journal of Cosmology and Astroparticle Physics, Vol. 2018, Issue 01
  • DOI: 10.1088/1475-7516/2018/01/003

The renormalization group and the ε expansion
journal, August 1974


Fast power spectrum estimation: Fast power
journal, November 2003


Mining weak lensing surveys
journal, August 2003