A Bayesian estimate of the skewness of the Cosmic Microwave Background

Abstract

We propose a formalism for estimating the skewness and angular power spectrum of a general Cosmic Microwave Background data set. We use the Edgeworth Expansion to define a non-Gaussian likelihood function that takes into account the anisotropic nature of the noise and the incompleteness of the sky coverage. The formalism is then applied to estimate the skewness of the publicly available 4 year Cosmic Background Explorer (COBE) Differential Microwave Radiometer data. We find that the data is consistent with a Gaussian skewness, and with isotropy. Inclusion of non Gaussian degrees of freedom has essentially no effect on estimates of the power spectrum, if each $C_{\ell }$ is regarded as a separate parameter or if the angular power spectrum is parametrized in terms of an amplitude (Q) and spectral index (n). Fixing the value of the angular power spectrum at its maxiumum likelihood estimate, the best fit skewness is $S=6.5\pm6.0\times10^4(\muK)^3$; marginalizing over Q the estimate of the skewness is $S=6.5\pm8.4\times10^4(\muK)^3$ and marginalizing over n one has $S=6.5\pm8.5\times10^4(\muK)^3$.

arXiv commentsubmitted to Astrophysical Journal Letters

References in corpus (12)

• 4-Year COBE DMR Cosmic Microwave Background Observations: Maps and Basic Results
• Nongaussian Isocurvature Perturbations from Inflation
• The Three--Point Correlation Function of the Cosmic Microwave Background in Inflationary Models
• Evidence for non-Gaussianity in the COBE DMR Four Year Sky Maps
• Tests for Non-Gaussian Statistics in the DMR Four-Year Sky Maps
• Evidence for Scale-Scale Correlations in the Cosmic Microwave Background Radiation
• On Determining the Spectrum of Primordial Inhomogeneity from the COBE DMR Sky Maps: I. Method
• Weakly Non-Linear Gaussian Fluctuations and the Edgeworth Expansion
• Statistics and Topology of the COBE DMR First Year Maps
• RMS Anisotropy in the COBE-DMR Four-Year Sky Maps
• Is the cosmic microwave background really non-Gaussian?
• Cosmic Variance of the Three-Point Correlation Function of the Cosmic Microwave Background

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