  We present a new method to constrain the dark matter halo density profiles of
disk galaxies. Our algorithm employs a Markov Chain Monte Carlo (MCMC) approach
to explore the parameter space of a general family of dark matter profiles. We
improve upon previous analyses by considering a wider range of halo profiles
and by explicitly identifying cases in which the data are insufficient to break
the degeneracies between the model parameters. We demonstrate the robustness of
our algorithm using artificial data sets and show that reliable estimates of
the halo density profile can be obtained from data of comparable quality to
those currently available for low surface brightness (LSB) galaxies. We present
our results in terms of physical quantities which are constrained by the data,
and find that the logarithmic slope of the halo density profile at the radius
of the innermost data point of a measured rotation curve can be strongly
constrained in LSB ([Vstar/Vobs]max ~ 0.16) galaxies. High surface brightness
galaxies ([Vstar/Vobs]max ~ 0.79) require additional information on the
mass-to-light ratio of the stellar population - our approach naturally
identifies those galaxies for which this is necessary. We apply our method to
observed data for the dwarf irregular galaxy DDO 154 and recover a logarithmic
halo slope of -0.39 +- 0.11 at a radius of 0.14 kpc. Our analysis validates
earlier estimates which were based on the fitting of a limited set of
individual halo models, but constitutes a more robust constraint than was
possible using other techniques since it marginalises over a wide range of halo
profiles.
