task in the Miriad software package, and determine a $\chi^2$ likelihood function, $\text{ln}\mathcal{L} = -\chi^2/2$, that incorporates the statistical weights of the visibilities. We make use of the [emcee]{} package [@foreman13] to sample the posterior probability distribution of the data conditioned on the model, and determine the best-fit parameter values and their uncertainties. We explore the posterior with 50,000 iterations ($100$ walkers and $5,000$ steps each) and check that the Gelman-Rubin statistic [@gelman14] is $\hat{R}<1.1$ for all parameters to ensure convergence.

We first fit the SMA observations and the ALMA observations separately, to examine the constraints provided by each dataset alone, and then fit the observations from both telescopes simultaneously, to examine the joint constraints. Table \[tab:par\] lists the best-fit parameters from each of these fits, together with their 68% uncertainties determined from the marginalized posterior probability distributions. For modeling the SMA observations alone, we adopt uniform priors for all parameters, in particular $0<R_\text{in}<R_\text{out}$, $F_\text{belt}>0$, and $-3<x<3$. When modeling the ALMA observations alone, informative constraints were not obtained for the outer radius or total flux parameters using these assumptions. In effect, the ALMA data allow the outer radius parameter to extend freely, with ever increasing total flux. This most likely 