The standard method for extracting cosmological parameters from the CMB is through the use of Maximum Likelihood methods. In general the likelihood function, , for a set of parameters, , is given by a hypothesis, , for the distribution function of the data set. In the case of uniform prior, and assuming a multivariate Gaussian distributed data set consistent with Inflationary models, the a posteriori probability distribution for the parameters is
where are the usual cosmological parameters we would like to determine. Examples of data are or and the statistics of the data are fully parametrised by the data covariance matrix, . For simplicity here we assume the data have zero means.