I have a project in which a Monte-Carlo method is used to find the optimal parameters for some model that is fit to a data set. I want to fit a model for the orbit of Mercury using this methods, but I can't find any data to fit it to. I have found a lot of papers on the orbit of Mercury that mention observational data, but no actual observational data. Where could I find data indicating the position of Mercury around the sun over a time period, or even a relatively accurate mathematical model from which I can generate my own data by defining it as a function that is stepped through some time interval?
The available astrometric data for Mercury come from meridian transit timings (right ascension and declination) and radar or spacecraft ranging (distance). NASA JPL has some here, and the French IMCCE has some here. To use those, you'll have to work out some geometry including the position of Earth in its own orbit.
For your purpose it may be easier to use numerical ephemerides via JPL HORIZONS or SPICE, or IMCCE Miriade or Multisat, which can output Cartesian coordinates if requested. Of course these are fit to observational data themselves. The underlying data files (e.g. DE430, INPOP17a) come with papers detailing sources, methods, uncertainties, etc.