  We consider the issue of hemispherical power asymmetry in the three-year WMAP
data, adopting a previously introduced modulation framework. Computing both
frequentist probabilities and Bayesian evidences, we find that the model
consisiting of an isotropic CMB sky modulated by a dipole field, gives a
substantially better fit to the observations than the purely isotropic model,
even when accounting for the larger prior volume. For the ILC map, the Bayesian
log-evidence difference is ~1.8 in favour of the modulated model, and the raw
improvement in maximum log-likelihood is 6.1. The best-fit modulation dipole
axis points toward (l,b) = (225 deg,-27 deg), and the modulation amplitude is
0.114, in excellent agreement with the results from the first-year analyses.
The frequentist probability of obtaining such a high modulation amplitude in an
isotropic universe is ~1%. These results are not sensitive to data set or sky
cut. Thus, the statistical evidence for a power asymmetry anomaly is both
substantial and robust, although not decisive, for the currently available
data. Increased sky coverage through better foreground handling and full-sky
and high-sensitivity polarization maps may shed further light on this issue.
