Example of a single-cloud (left) and two-cloud (right) simulated data set. We show the stellar q_V (green circles) and u_V (blue diamonds) Stokes parameters as a function of distance modulus (μ_i) Top and bottom panels show the same data set. Top panels do not include observational noise (they are the “true” data points) while bottom panels do include uncertainties in both parallax and polarization (shown with errorbars). The vertical red lines indicate the input distance modulus of the clouds. The horizontal green and dashed-purple lines indicate the input (cumulative) mean Stokes parameters (q_C and u_C, respectively) before the inclusion of intrinsic scatter and observational noise, i.e., in Eq. (1).