First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Parameter Estimation Methodology

Abstract

We describe our methodology for comparing the WMAP measurements of the cosmic microwave background (CMB) and other complementary data sets to theoretical models. The unprecedented quality of the WMAP data, and the tight constraints on cosmological parameters that are derived, require a rigorous analysis so that the approximations made in the modeling do not lead to significant biases. We describe our use of the likelihood function to characterize the statistical properties of the microwave background sky. We outline the use of the Monte Carlo Markov Chains to explore the likelihood of the data given a model to determine the best fit cosmological parameters and their uncertainties. We add to the WMAP data the l>~700 CBI and ACBAR measurements of the CMB, the galaxy power spectrum at z~0 obtained from the 2dF galaxy redshift survey (2dFGRS), and the matter power spectrum at z~3 as measured with the Ly alpha forest. These last two data sets complement the CMB measurements by probing the matter power spectrum of the nearby universe. Combining CMB and 2dFGRS requires that we include in our analysis a model for galaxy bias, redshift distortions, and the non-linear growth of structure. We show how the statistical and systematic uncertainties in the model and the data are propagated through the full analysis.

Replaced with version with final edits for ApJ. One of thirteen companion papers on first-year WMAP results; 38 pages, 8 figures; a version with higher quality figures is available at http://lambda.gsfc.nasa.gov/

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• The Microwave Anisotropy Probe (MAP) Mission
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• First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Beam Profiles and Window Functions
• Design, Implementation and Testing of the MAP Radiometers
• Weak lensing study of galaxy biasing
• The Optical Design and Characterization of the Microwave Anisotropy Probe
• First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: On-Orbit Radiometer Characterization
• First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Galactic Signal Contamination from Sidelobe Pickup

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• A measurement of the Integrated Sachs-Wolfe Effect with the Rapid ASKAP Continuum Survey
• Statistical characteristics of observed Ly-$\alpha$ forest and the shape of initial power spectrum
• Statistical characteristics of observed Ly-$\alpha$ forest and the shape of linear power spectrum
• Gravitino dark matter from gluino late decay in split supersymmetry
• Cosmological Constraints on Rapid Roll Inflation
• The Atacama Cosmology Telescope: Semi-Analytic Covariance Matrices for the DR6 CMB Power Spectra
• Efficient cosmological parameter sampling using sparse grids
• Detection of transplanckian effects in the cosmic microwave background
• Observational prospects for phase transitions at LISA: Fisher matrix analysis
• Evolution of the CMB Power Spectrum Across WMAP Data Releases: A Nonparametric Analysis
• MOA-2012-BLG-505Lb: A super-Earth mass planet probably in the Galactic bulge
• Doppler-beaming in the Kepler light curve of LHS 6343 A
• Cosmological Parameters from a re-analysis of the WMAP-7 low resolution maps
• Density perturbations from both the inflaton and the curvaton
• Constraining the reionization history with large angle CMB polarization
• A very extended reionization epoch ?
• General solutions of the leakage in integral transforms and applications to the EB-leakage and detection of the cosmological gravitational wave background
• Mapping the Cosmological Confidence Ball Surface
• Well behaved class of Heintzmann's solution within $f(R,T)$ framework
• Primordial Black Hole Pair Creation Probability in Modified Gravitational Theory
• Probability for Primordial Black Holes Pair in 1/R Gravity
• Status and Perspectives of Neutrino Physics
• Probing the Galactic Potential with Next-Generation Observations of Disk Stars
• Caching and Interpolated Likelihoods: Accelerating Cosmological Monte Carlo Markov Chains
• Density fluctuations on mm and Mpc scales
• Constraints on the Sum of Neutrino Masses from Cosmology and their impact on world neutrino data
• CMB likelihood approximation for banded probability distributions
• Cosmological constraints from galaxy clustering
• The two-and three-point correlation functions of the polarized five-year WMAP sky maps
• A model of inflation independent of the initial conditions, with bounded number of e-folds and n_s larger orsmaller than one
• Is it possible to observationally distinguish adiabatic Quartessence from LambdaCDM?
• ParamANN: A Neural Network to Estimate Cosmological Parameters for $\Lambda$CDM Universe Using Hubble Measurements
• OGLE-2015-BLG-1649Lb: A gas giant planet around a low-mass dwarf
• DeepSSM: an emulator of gravitational wave spectra from sound waves during cosmological first-order phase transitions
• Cosmoglobe: Towards end-to-end CMB cosmological parameter estimation without likelihood approximations
• Effects of Smoothing Functions in Cosmological Counts-in-Cells Analysis
• OGLE-2014-BLG-0319: A Sub-Jupiter-Mass Planetary Event Encountered Degeneracy with Different Mass Ratios and Lens-Source Relative Proper Motions
• ForestFlow: predicting the Lyman-$\alpha$ forest clustering from linear to nonlinear scales
• New Constraints on Dark Energy
• Faint Galaxy Number Counts in the Durhamand SDSS Catalogues
• Particle Physics in the Sky and Astrophysics Underground: Connecting the Universe's Largest and Smallest Scales
• Cosmological model with Born-Infeld type scalar field
• Pico: Parameters for the Impatient Cosmologist
• Probing the last scattering surface through the recent and future CMB observations
• A Python compressed low-$\ell$ Planck likelihood for temperature and polarization
• Angular Power Spectrum in Modular Invariant Inflation Model
• Evaluation of multi-parameter likelihoods through iteration of two-dimensional slices
• Optimisation of the Population Monte Carlo algorithm: Application to constraining isocurvature models with cosmic microwave background data
• Integrated Markov Chain Monte Carlo (MCMC) analysis of primordial non-Gaussianity (f_NL) in the recent CMB data
• Maps of the Cosmos: The Cosmic Microwave Background
• Discrepancies between observational data and theoretical forecast in single field slow roll inflation
• Mapping the dark matter using weak lensing
• Observational constraints on a decaying cosmological term
• CMB Observational Techniques and Recent Results