A Bayesian estimate of the skewness of the cosmic microwave background

We propose a formalism for estimating the skewness and angular power spectr um of a general cosmic microwave background data set. We use the Edgeworth expansion to define a non-Gaussian likelihood function that takes into acco unt the anisotropic nature of the noise and the incompleteness of the sky c overage. The formalism is then applied to estimate the skewness of the publ icly available 4 yr COBE Differential. Microwave Radiometer (DMR) data. We find that the data is consistent with a Gaussian skewness, and with isotrop y. Inclusion of non-Gaussian degrees of freedom has essentially no effect o n estimates of the power spectrum, if each C-iota 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 maximum-likelihood estimate, the best-fit skewness is S = 6.5 +/- 6.0 x 10(4) mu K-3; marginalizing over Q, the estimate of the skewn ess is S = 6.5 +/- 8.4 x 10(4) mu K-3, and marginalizing over n one has S = 6.5 +/- 8.5 x 10(4) mu K-3.