  Recent attempts to constrain cosmological variation in the fine structure
constant, alpha, using quasar absorption lines have yielded two statistical
samples which initially appear to be inconsistent. One of these samples was
subsequently demonstrated to not pass consistency tests; it appears that the
optimisation algorithm used to fit the model to the spectra failed.
Nevertheless, the results of the other hinge on the robustness of the spectral
fitting program VPFIT, which has been tested through simulation but not through
direct exploration of the likelihood function. We present the application of
Markov Chain Monte Carlo (MCMC) methods to this problem, and demonstrate that
VPFIT produces similar values and uncertainties for (Delta alpha)/(alpha), the
fractional change in the fine structure constant, as our MCMC algorithm, and
thus that VPFIT is reliable.
