  We use Bayesian statistics and Markov chain Monte Carlo (MCMC) techniques to
construct dynamical models for the spiral galaxy NGC 6503. The constraints
include surface brightness profiles which display a Freeman Type II structure;
HI and ionized gas rotation curves; the stellar rotation, which is nearly
coincident with the ionized gas curve; and the line of sight stellar
dispersion, with a sigma-drop at the centre. The galaxy models consist of a
Sersic bulge, an exponential disc with an optional inner truncation and a
cosmologically motivated dark halo. The Bayesian/MCMC technique yields the
joint posterior probability distribution function for the input parameters. We
examine several interpretations of the data: the Type II surface brightness
profile may be due to dust extinction, to an inner truncated disc or to a ring
of bright stars; and we test separate fits to the gas and stellar rotation
curves to determine if the gas traces the gravitational potential. We test each
of these scenarios for bar stability, ruling out dust extinction. We also find
that the gas likely does not trace the gravitational potential, since the
predicted stellar rotation curve is then inconsistent with the observed stellar
rotation curve. The disc is well fit by an inner-truncated profile, but the
possibility of ring formation by a bar to reproduce the Type II profile is also
a realistic model. We further find that the halo must have a cuspy profile with
gamma > 1; the bulge has a lower M/L than the disc, suggesting a star forming
component in the centre of the galaxy; and the bulge, as expected for this late
type galaxy, has a low Sersic index with n_b~1-2, suggesting a formation
history dominated by secular evolution.
