Professor Pedro Ferreira

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 $S=6.5\pm8.5\times10^4(\muK)^3$.

Abstract:

To correctly analyse data sets from current microwave detection technology, one is forced to estimate the sky signal and experimental noise simultaneously. Given a time-ordered data set we propose a formalism and method for estimating the signal and associated errors without prior knowledge of the noise power spectrum. We derive the method using a Bayesian formalism and relate it to the standard methods; in particular we show how this leads to a change in the estimate of the noise covariance matrix of the sky signal. We study the convergence and accuracy of the method on two mock observational strategies and discuss its application to a currently-favoured calibration procedure.