The Cosmic Microwave Background (CMB) is the main source of information we have about the early Universe. The importance of estimating the spatial power spectrum of the cosmic microwave background is the due to the wealth of information it yields about the physical properties of the Universe. These fundamental properties leave different statistical patterns of hot and cold spots on the sky at microwave frequencies.

CMB power spectrum estimation, and estimation of error bars, is complicated by incomplete sky coverage; non-homogeneous, correlated instrumental noise; and foreground emission that obscures the critical signal. Jeff Jewell and collaborators have developed a Monte Carlo approach for a fully Bayesian solution to the analysis of the CMB. This method has been generalized to be able to handle the massive amount of data being returned from the Planck satellite, a joint NASA and European Space Agency mission for which JPL plays a central role in detector and algorithm development.

The method uses a cutting-edge high-dimensional Markov chain Monte Carlo (MCMC) statistical analysis. The approach allows us to derive means and error bars for spherical harmonic coefficients. Having accurate error bars is critical for checks of cosmological theories. The results are a core part of Planck science data releases.

## Selected Publications

Pietrobon, Davide, Gorski, Krzysztof M, Bartlett, James, Banday, A J, Dobler, Gregory, Colombo, Loris P L, Hildebrandt, Sergi R, Jewell, Jeffrey B, Pagano, Luca, Rocha, Graca, Eriksen, Hans Kristian, Saha, Rajib, and Lawrence, Charles R (2012). “Analysis of WMAP 7 Year Temperature Data: Astrophysics of the Galactic Haze,” The Astrophysical Journal, 755(1), p. 69.

Mennella, A, et al. (2011). “Planck early results. III. First assessment of the Low Frequency Instrument in-flight performance,” Astronomy and Astrophysics, 536, pp. A3.

Tauber, J. A,. et al. (2010). “Planck pre-launch status: The Planck mission,” Astronomy and Astrophysics, 520, pp. A1.

Dickinson, C, Eriksen, H K, Banday, A J, Jewell, J B, Górski, K M, Huey, G, Lawrence, C R, O'Dwyer, I J, and Wandelt, B D (2009). “Bayesian Component Separation and Cosmic Microwave Background Estimation for the Five-Year WMAP Temperature Data,” The Astrophysical Journal, 705(2), pp. 1607–1623.

Jewell, J B, Eriksen, H K, Wandelt, B D, O'Dwyer, I J, Huey, Greg, and Górski, K M (2009). “A Markov Chain Monte Carlo Algorithm for Analysis of Low Signal-To-Noise Cosmic Microwave Background Data,” The Astrophysical Journal, 697(1), pp. 258–268.

Rudjord, \O, Groeneboom, N E, Eriksen, H K, Huey, Greg, Górski, K M, and Jewell, J B (2009). “Cosmic Microwave Background Likelihood Approximation by a Gaussianized Blackwell-Rao Estimator,” The Astrophysical Journal, 692(2), pp. 1669–1677.

Groeneboom, N E, Eriksen, H K, Gorski, K, Huey, G, Jewell, Jeffrey, and Wandelt, B (2009). “Bayesian Analysis of White Noise Levels in the Five-Year WMAP Data,” The Astrophysical Journal Letters, 702(1), pp. L87–L90.

Eriksen, H K, Jewell, J B, Dickinson, C, Banday, A J, Górski, K M, and Lawrence, C R (2008). “Joint Bayesian component separation and CMB power spectrum estimation,” The Astrophysical Journal, 676(1), p. 10.

Eriksen, H K, Dickinson, C, Jewell, J B, Banday, A J, Górski, K M, and Lawrence, C R (2008). “The Joint Large-Scale Foreground-CMB Posteriors of the 3 Year WMAP Data,” The Astrophysical Journal, 672(2), pp. L87–L90.

Eriksen, H K, Huey, Greg, Saha, R, Hansen, F K, Dick, J, Banday, A J, Górski, K M, Jain, P, Jewell, J B, Knox, L, Larson, D L, O'Dwyer, I J, Souradeep, T, and Wandelt, B D (2007). “A Reanalysis of the 3 Year Wilkinson Microwave Anisotropy Probe Temperature Power Spectrum and Likelihood,” The Astrophysical Journal, 656(2), pp. 641–652.

Larson, D L, Eriksen, H K, Wandelt, B D, Górski, K M, Huey, G, Jewell, J B, and O'Dwyer, I J (2007). “Estimation of polarized power spectra by Gibbs sampling,” The Astrophysical Journal, 656(2), p. 653.

Eriksen, H K, Huey, Greg, Banday, A J, Górski, K M, Jewell, J B, O'Dwyer, I J, and Wandelt, B D (2007). “Bayesian Analysis of the Low-Resolution Polarized 3 Year WMAP Sky Maps,” The Astrophysical Journal, 665(1), pp. L1–L4.

Chu, M, Eriksen, H, Knox, L, Gorski, K, Jewell, Jeffrey, Larson, D, O'Dwyer, I, and Wandelt, B (2005). “Cosmological parameter constraints as derived from the Wilkinson Microwave Anisotropy Probe data via Gibbs sampling and the Blackwell-Rao estimator,” Physical Review D, 71(10), p. 103002.

O'Dwyer, I J, Eriksen, H K, Wandelt, B D, Jewell, J B, Larson, D L, Górski, K M, Banday, A J, Levin, S, and Lilje, P B (2004). “Bayesian Power Spectrum Analysis of the First-Year Wilkinson Microwave Anisotropy Probe Data,” The Astrophysical Journal, 617(2), pp. L99–L102.

Jewell, Jeffrey, Levin, S, and Anderson, C H (2004). “Application of Monte Carlo Algorithms to the Bayesian Analysis of the Cosmic Microwave Background,” The Astrophysical Journal, 609(1), pp. 1–14.

Eriksen, H K, O'Dwyer, I J, Jewell, J B, Wandelt, B D, Larson, D L, Górski, K M, Levin, S, Banday, A J, and Lilje, P B (2004). “Power Spectrum Estimation from High-Resolution Maps by Gibbs Sampling,” The Astrophysical Journal Supplement Series, 155(2), pp. 227–241.

Jewell, Jeffrey (2001). “A Statistical Characterization of Galactic Dust Emission as a Non-Gaussian Foreground of the Cosmic Microwave Background,” The Astrophysical Journal, 557(2), pp. 700–713.

Jewell, Jeffrey, Lawrence, C R, and Levin, S (1999). “Bayesian Approach to Foreground Removal,” Microwave Foregrounds, vol. 181, p. 357.