  We describe a sampling method to estimate the polarized CMB signal from
observed maps of the sky. We use a Metropolis-within-Gibbs algorithm to
estimate the polarized CMB map, containing Q and U Stokes parameters at each
pixel, and its covariance matrix. These can be used as inputs for cosmological
analyses. The polarized sky signal is parameterized as the sum of three
components: CMB, synchrotron emission, and thermal dust emission. The polarized
Galactic components are modeled with spatially varying power law spectral
indices for the synchrotron, and a fixed power law for the dust, and their
component maps are estimated as by-products. We apply the method to simulated
low resolution maps with pixels of side 7.2 degrees, using diagonal and full
noise realizations drawn from the WMAP noise matrices. The CMB maps are
recovered with goodness of fit consistent with errors. Computing the likelihood
of the E-mode power in the maps as a function of optical depth to reionization,
tau, for fixed temperature anisotropy power, we recover tau=0.091+-0.019 for a
simulation with input tau=0.1, and mean tau=0.098 averaged over 10 simulations.
A `null' simulation with no polarized CMB signal has maximum likelihood
consistent with tau=0. The method is applied to the five-year WMAP data, using
the K, Ka, Q and V channels. We find tau=0.090+-0.019, compared to
tau=0.086+-0.016 from the template-cleaned maps used in the primary WMAP
analysis. The synchrotron spectral index, beta, averaged over high
signal-to-noise pixels with standard deviation sigma(beta)<0.25, but excluding
~6% of the sky masked in the Galactic plane, is -3.03+-0.04. This estimate does
not vary significantly with Galactic latitude, although includes an informative
prior.
