of the type used by Kormendy (1977). Inner truncated disc profiles may be due to dust extinction against an exponential disc (MacArthur et al. 2003); they may be intrinsic to the density profile; or they may be due to a ring of bright stars which does not trace the mass. We explore these possibilities by testing models numerically under each scenario for bar formation. The coincidence of gas and stellar rotation curves also deserves attention as it suggests far less asymmetric drift than predicted. Thus, we wish to understand whether gas follows circular orbits that trace the gravitational potential, or whether it has its own asymmetric drift. We investigate this issue by testing two different ways of fitting the rotation curves: by fitting the stellar rotation alone and using the asymmetric drift to calculate the circular velocity; and by fitting the gas alone assuming it traces the circular velocity. Our aim is to construct dynamical models for each of these scenarios and test them via N − body simulations. We use the GalactICS model from Widrow et al. (2008, hereafter WPD) defined in terms of distribution functions for the disc, bulge and halo. The halo allows for a cusp or a core, and the bulge follows a S´ ersic (1968) profile. The disc surface density profile is exponential with an optional inner truncation. The large number of parameters makes finding a fit to the data a challenging exercise. A number of techniques have been developed to determine best-fit parameters in such complex spaces – notably, maximum likelihood techniques which involve minimizing the χ 2 value. One promising approach which improves upon the maximum likelihood method employs Bayes’ theorem and a Markov chain Monte Carlo (MCMC) technique to survey the relevant parameter space. Bayes’ theorem provides a method of determining the posterior probability of a hypothesis based on both the likelihood function and prior information about the input parameters; MCMC provides for a way to survey the parameter space. In conjunction, the two techniques provide the joint posterior probability distribution function (PDF) of the mul- tidimensional parameter space; the marginal posterior PDF for any parameter (and hence its formal mean and error bars) are obtained by marginalizing over nuisance parameters. This technique yields realistic constraints on the model parameters, including (but not limited to) the halo cusp, the disc and bulge M/L ratios, masses for each component, inner trun- cation parameters, and bulge S´ ersic index. Similar techniques have been used, for example, to determine cosmological parameters (Tegmark et al. 2004; Percival 2005; Corless & King 2008). In this work we build dynamical models for NGC 6503 using a Bayesian/MCMC method. We fit several data sets for this galaxy simultaneously in order to obtain as complete a picture of the galaxy as possible; however, the lack of a bar provides a further constraint. There- fore, we also obtain the stability parameters X and Q for our models. The X − parameter determines global stability to multi-armed modes (Toomre 1981) and the Q − parameter de- 3