  Measuring the masses of protoplanetary disks is crucial for understanding
their planet-forming potential. Typically, dust masses are derived from
(sub-)millimeter flux density measurements plus assumptions for the opacity,
temperature, and optical depth of the dust. Here we use radiative transfer
models to quantify the validity of these assumptions with the aim of improving
the accuracy of disk dust mass measurements. We first carry out a controlled
exploration of disk parameter space. We find that the disk temperature is a
strong function of disk size, while the optical depth depends on both disk size
and dust mass. The millimeter-wavelength spectral index can be significantly
shallower than the naive expectation due to a combination of optical depth and
deviations from the Rayleigh-Jeans regime. We fit radiative transfer models to
the spectral energy distributions (SEDs) of 132 disks in the Taurus-Auriga
region using a Markov chain Monte Carlo approach. We used all available data to
produce the most complete SEDs used in any extant modeling study. We perform
the fitting twice: first with unconstrained disk sizes and again imposing the
disk size--brightness relation inferred for sources in Taurus. This constraint
generally forces the disks to be smaller, warmer, and more optically thick.
From both sets of fits, we find disks to be $\sim$1--5 times more massive than
when derived using (sub-)millimeter measurements and common assumptions. With
the uncertainties derived from our model fitting, the previously measured dust
mass--stellar mass correlation is present in our study but only significant at
the 2$\sigma$ level.
