A significant fraction of quasars exhibit blueshifted broad

absorption lines (BALs) in their rest-UV spectra, indicating powerful

outflows emerging from the central engine. Despite more than 50 years

of study, the physical conditions of the outflowing gas are poorly

understood.  Our group has developed SimBAL, a novel spectral

synthesis fitting method for BAL quasar spectra that uses Bayesian

model calibration to compare synthetic to observed spectra. I will

describe the construction of SimBAL, and illustrate its unique

strengths by discussing the results from several projects.