Extreme data compression for the CMB
Abstract
We apply the KarhunenLoéve methods to cosmic microwave background (CMB) data sets, and show that we can recover the input cosmology and obtain the marginalized likelihoods in Λ cold dark matter cosmologies in under a minute, much faster than Markov chain Monte Carlo methods. This is achieved by forming a linear combination of the power spectra at each multipole l, and solving a system of simultaneous equations such that the Fisher matrix is locally unchanged. Instead of carrying out a full likelihood evaluation over the whole parameter space, we need evaluate the likelihood only for the parameter of interest, with the data compression effectively marginalizing over all other parameters. The weighting vectors contain insight about the physical effects of the parameters on the CMB anisotropy power spectrum C _{l}. The shape and amplitude of these vectors give an intuitive feel for the physics of the CMB, the sensitivity of the observed spectrum to cosmological parameters, and the relative sensitivity of different experiments to cosmological parameters. We test this method on exact theory C _{l} as well as on a Wilkinson Microwave Anisotropy Probe (WMAP)like CMB data set generated from a random realization of a fiducial cosmology, comparing the compression results tomore »
 Authors:

 Univ. of Chicago, Chicago, IL (United States)
 Univ. of Chicago, Chicago, IL (United States); Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)
 Publication Date:
 Research Org.:
 Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC), High Energy Physics (HEP) (SC25)
 OSTI Identifier:
 1253181
 Alternate Identifier(s):
 OSTI ID: 1249799
 Report Number(s):
 FERMILABPUB15542A; arXiv:1512.00072
Journal ID: ISSN 24700010; PRVDAQ; 1407435
 Grant/Contract Number:
 AC0207CH11359; FG0213ER41958; FG0295ER40896
 Resource Type:
 Journal Article: Accepted Manuscript
 Journal Name:
 Physical Review D
 Additional Journal Information:
 Journal Volume: 93; Journal Issue: 8; Journal ID: ISSN 24700010
 Publisher:
 American Physical Society (APS)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 79 ASTRONOMY AND ASTROPHYSICS
Citation Formats
Zablocki, Alan, and Dodelson, Scott. Extreme data compression for the CMB. United States: N. p., 2016.
Web. doi:10.1103/PhysRevD.93.083525.
Zablocki, Alan, & Dodelson, Scott. Extreme data compression for the CMB. United States. doi:10.1103/PhysRevD.93.083525.
Zablocki, Alan, and Dodelson, Scott. Thu .
"Extreme data compression for the CMB". United States. doi:10.1103/PhysRevD.93.083525. https://www.osti.gov/servlets/purl/1253181.
@article{osti_1253181,
title = {Extreme data compression for the CMB},
author = {Zablocki, Alan and Dodelson, Scott},
abstractNote = {We apply the KarhunenLoéve methods to cosmic microwave background (CMB) data sets, and show that we can recover the input cosmology and obtain the marginalized likelihoods in Λ cold dark matter cosmologies in under a minute, much faster than Markov chain Monte Carlo methods. This is achieved by forming a linear combination of the power spectra at each multipole l, and solving a system of simultaneous equations such that the Fisher matrix is locally unchanged. Instead of carrying out a full likelihood evaluation over the whole parameter space, we need evaluate the likelihood only for the parameter of interest, with the data compression effectively marginalizing over all other parameters. The weighting vectors contain insight about the physical effects of the parameters on the CMB anisotropy power spectrum Cl. The shape and amplitude of these vectors give an intuitive feel for the physics of the CMB, the sensitivity of the observed spectrum to cosmological parameters, and the relative sensitivity of different experiments to cosmological parameters. We test this method on exact theory Cl as well as on a Wilkinson Microwave Anisotropy Probe (WMAP)like CMB data set generated from a random realization of a fiducial cosmology, comparing the compression results to those from a full likelihood analysis using CosmoMC. Furthermore, after showing that the method works, we apply it to the temperature power spectrum from the WMAP sevenyear data release, and discuss the successes and limitations of our method as applied to a real data set.},
doi = {10.1103/PhysRevD.93.083525},
journal = {Physical Review D},
issn = {24700010},
number = 8,
volume = 93,
place = {United States},
year = {2016},
month = {4}
}
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