We introduce a Bayesian approach coupled with a Markov Chain Monte Carlo (MCMC) method and the maximum likelihood statistic for fitting the profiles of narrow absorption lines (NALs) in quasar spectra. This method also incorporates overlap between different absorbers. We illustrate and test this method by fitting models to a mini-broad (mini-BAL) and six NAL profiles in four spectra of the quasar UM675 taken over a rest-frame interval of 4.24 years. Our fitting results are consistent with past results for the mini-BAL system in this quasar by Hamann et al. (1997b). We also measure covering factors ($C_{rm f}$) for two narrow components in the CIV and NV mini-BALs and their overlap covering factor with the broad component. We find that $C_{rm f}$(NV) is always larger than $C_{rm f}$(CIV) for the broad component, while the opposite is true for the narrow components in the mini-BAL system. This could be explained if the broad and narrow components originated in gas at different radial distances, but it seems more likely to be due to them produced by gas at the same distance but with different gas densities (i.e., ionization states). The variability detected only in the broad absorption component in the mini-BAL system is probably due to gas motion since both $C_{rm f}$(CIV) and $C_{rm f}$(NV) vary. We determine for the first time that multiple absorbing clouds (i.e., a broad and two narrow components) overlap along our line of sight. We conclude that the new method improves fitting results considerably compared to previous methods.
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