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 welldefined hybrid likelihood estimator, merging two independent (e.g., low and highl) 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 casebycase basis, we recommend our new hybridization scheme for future experiments for statistical selfconsistency reasons. Second, we use the same expression tomore »
 Authors:

 Institute of Theoretical Astrophysics, University of Oslo, P.O. Box 1029 Blindern, N0315 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 0004637X
 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., Email: eirik.gjerlow@astro.uio.no. COSMIC MICROWAVE BACKGROUND LIKELIHOOD APPROXIMATION FOR BANDED PROBABILITY DISTRIBUTIONS. United States: N. p., 2013.
Web. doi:10.1088/0004637X/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., Email: eirik.gjerlow@astro.uio.no. COSMIC MICROWAVE BACKGROUND LIKELIHOOD APPROXIMATION FOR BANDED PROBABILITY DISTRIBUTIONS. United States. doi:10.1088/0004637X/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., Email: eirik.gjerlow@astro.uio.no. Sun .
"COSMIC MICROWAVE BACKGROUND LIKELIHOOD APPROXIMATION FOR BANDED PROBABILITY DISTRIBUTIONS". United States. doi:10.1088/0004637X/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., Email: 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 welldefined hybrid likelihood estimator, merging two independent (e.g., low and highl) 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 casebycase basis, we recommend our new hybridization scheme for future experiments for statistical selfconsistency reasons. Second, we use the same expression to improve the convergence rate of the BlackwellRao likelihood estimator, reducing the required number of Monte Carlo samples by several orders of magnitude, and thereby extend it to highl applications.},
doi = {10.1088/0004637X/777/2/150},
journal = {Astrophysical Journal},
issn = {0004637X},
number = 2,
volume = 777,
place = {United States},
year = {2013},
month = {11}
}