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

Title: COSMIC MICROWAVE BACKGROUND LIKELIHOOD APPROXIMATION FOR BANDED PROBABILITY DISTRIBUTIONS

Abstract

We investigate sets of random variables that can be arranged sequentially such that a given variable only depends conditionally on its immediate predecessor. For such sets, we show that the full joint probability distribution may be expressed exclusively in terms of uni- and bivariate marginals. Under the assumption that the cosmic microwave background (CMB) power spectrum likelihood only exhibits correlations within a banded multipole range, Δl{sub C}, we apply this expression to two outstanding problems in CMB likelihood analysis. First, we derive a statistically well-defined hybrid likelihood estimator, merging two independent (e.g., low- and high-l) likelihoods into a single expression that properly accounts for correlations between the two. Applying this expression to the Wilkinson Microwave Anisotropy Probe (WMAP) likelihood, we verify that the effect of correlations on cosmological parameters in the transition region is negligible in terms of cosmological parameters for WMAP; the largest relative shift seen for any parameter is 0.06σ. However, because this may not hold for other experimental setups (e.g., for different instrumental noise properties or analysis masks), but must rather be verified on a case-by-case basis, we recommend our new hybridization scheme for future experiments for statistical self-consistency reasons. Second, we use the same expression tomore » improve the convergence rate of the Blackwell-Rao likelihood estimator, reducing the required number of Monte Carlo samples by several orders of magnitude, and thereby extend it to high-l applications.« less

Authors:
; ; ; ;  [1]; ; ; ;
  1. Institute of Theoretical Astrophysics, University of Oslo, P.O. Box 1029 Blindern, N-0315 Oslo (Norway)
Publication Date:
OSTI Identifier:
22270571
Resource Type:
Journal Article
Journal Name:
Astrophysical Journal
Additional Journal Information:
Journal Volume: 777; Journal Issue: 2; Other Information: Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0004-637X
Country of Publication:
United States
Language:
English
Subject:
79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; ANISOTROPY; APPROXIMATIONS; ASTROPHYSICS; BACKGROUND RADIATION; CORRELATIONS; COSMOLOGY; DATA ANALYSIS; MONTE CARLO METHOD; PROBABILITY; RANDOMNESS; RELICT RADIATION

Citation Formats

Gjerløw, E., Mikkelsen, K., Eriksen, H. K., Næss, S. K., Seljebotn, D. S., Górski, K. M., Huey, G., Jewell, J. B., Rocha, G., and Wehus, I. K., E-mail: eirik.gjerlow@astro.uio.no. COSMIC MICROWAVE BACKGROUND LIKELIHOOD APPROXIMATION FOR BANDED PROBABILITY DISTRIBUTIONS. United States: N. p., 2013. Web. doi:10.1088/0004-637X/777/2/150.
Gjerløw, E., Mikkelsen, K., Eriksen, H. K., Næss, S. K., Seljebotn, D. S., Górski, K. M., Huey, G., Jewell, J. B., Rocha, G., & Wehus, I. K., E-mail: eirik.gjerlow@astro.uio.no. COSMIC MICROWAVE BACKGROUND LIKELIHOOD APPROXIMATION FOR BANDED PROBABILITY DISTRIBUTIONS. United States. doi:10.1088/0004-637X/777/2/150.
Gjerløw, E., Mikkelsen, K., Eriksen, H. K., Næss, S. K., Seljebotn, D. S., Górski, K. M., Huey, G., Jewell, J. B., Rocha, G., and Wehus, I. K., E-mail: eirik.gjerlow@astro.uio.no. Sun . "COSMIC MICROWAVE BACKGROUND LIKELIHOOD APPROXIMATION FOR BANDED PROBABILITY DISTRIBUTIONS". United States. doi:10.1088/0004-637X/777/2/150.
@article{osti_22270571,
title = {COSMIC MICROWAVE BACKGROUND LIKELIHOOD APPROXIMATION FOR BANDED PROBABILITY DISTRIBUTIONS},
author = {Gjerløw, E. and Mikkelsen, K. and Eriksen, H. K. and Næss, S. K. and Seljebotn, D. S. and Górski, K. M. and Huey, G. and Jewell, J. B. and Rocha, G. and Wehus, I. K., E-mail: eirik.gjerlow@astro.uio.no},
abstractNote = {We investigate sets of random variables that can be arranged sequentially such that a given variable only depends conditionally on its immediate predecessor. For such sets, we show that the full joint probability distribution may be expressed exclusively in terms of uni- and bivariate marginals. Under the assumption that the cosmic microwave background (CMB) power spectrum likelihood only exhibits correlations within a banded multipole range, Δl{sub C}, we apply this expression to two outstanding problems in CMB likelihood analysis. First, we derive a statistically well-defined hybrid likelihood estimator, merging two independent (e.g., low- and high-l) likelihoods into a single expression that properly accounts for correlations between the two. Applying this expression to the Wilkinson Microwave Anisotropy Probe (WMAP) likelihood, we verify that the effect of correlations on cosmological parameters in the transition region is negligible in terms of cosmological parameters for WMAP; the largest relative shift seen for any parameter is 0.06σ. However, because this may not hold for other experimental setups (e.g., for different instrumental noise properties or analysis masks), but must rather be verified on a case-by-case basis, we recommend our new hybridization scheme for future experiments for statistical self-consistency reasons. Second, we use the same expression to improve the convergence rate of the Blackwell-Rao likelihood estimator, reducing the required number of Monte Carlo samples by several orders of magnitude, and thereby extend it to high-l applications.},
doi = {10.1088/0004-637X/777/2/150},
journal = {Astrophysical Journal},
issn = {0004-637X},
number = 2,
volume = 777,
place = {United States},
year = {2013},
month = {11}
}