  We derive a general expression for the probability of observing deviations
from statistical isotropy in the cosmic microwave background (CMB) if the
primordial fluctuations are non-Gaussian and extend to superhorizon scales. The
primary motivation is to properly characterize the monopole and dipole
modulations of the primordial power spectrum that are generated by the coupling
between superhorizon and subhorizon perturbations. Unlike previous proposals
for generating the hemispherical power asymmetry, we do not assume that the
power asymmetry results from a single large superhorizon mode. Instead, we
extrapolate the observed power spectrum to superhorizon scales and compute the
power asymmetry that would result from a specific realization of non-Gaussian
perturbations on scales larger than the observable universe. Our study
encompasses many of the scenarios that have been put forward as possible
explanations for the CMB hemispherical power asymmetry. We confirm our analytic
predictions for the probability of a given power asymmetry by comparing them to
numerical realizations of CMB maps. We find that non-local models of
non-Gaussianity and scale-dependent local non-Gaussianity produce
scale-dependent modulations of the power spectrum, thereby potentially
producing both a monopolar and a dipolar power modulation on large scales. We
then provide simple examples of finding the posterior distributions for the
parameters of the bispectrum from the observed monopole and dipole modulations.
