We use Bayesian component estimation methods to examine the prospects for large-scale polarized map and cosmological parameter estimation with simulated Planck data assuming simplified white noise properties .
The sky signal is parametrized as the sum of the CMB , synchrotron emission , and thermal dust emission .
The synchrotron and dust components are modelled as power-laws , with a spatially varying spectral index for synchrotron and a uniform index for dust .
Using the Gibbs sampling technique , we estimate the linear polarisation Q and U posterior amplitudes of the CMB , synchrotron and dust maps as well as the two spectral indices in \sim 4 ^ { \circ } pixels .
We use the recovered CMB map and its covariance in an exact pixel likelihood algorithm to estimate the optical depth to reionization \tau , the tensor-to-scalar ratio r , and to construct conditional likelihood slices for C _ { \ell } ^ { EE } and C _ { \ell } ^ { BB } .
Given our foreground model , we find \sigma ( \tau ) \approx 0.004 for \tau = 0.1 , \sigma ( r ) \approx 0.03 for a model with r = 0.1 , and a 95 % upper limit of r < 0.02 for r = 0.0 .