Markov chain Monte Carlo methods applied to photometric spot modeling

I demonstrate that Markov chain Monte Carlo methods can be used very effectively to determine best-fit values, uncertainties, and possible correlations or degeneracies in the fitted parameters of photometric spot modeling. Details of the Markov chain Monte Carlo methods applied here are briefly described, including the Metropolis-Hastings algorithm and the tests that are used to ensure proper convergence and mixing. This Markov chain Monte Carlo functionality is applied to recent observations of epsilon Eridani by the Microvariablity and Oscillations of Stars (MOST) satellite, and the two-spot solution showing differential rotation, as discussed in B. Croll et al. Conclusions in the latter are largely confirmed, but a strong correlation between the inclination and other fitted parameters is noted. The Markov chain Monte Carlo functionality has been included in StarSpotz, a freely available program for photometric spot modeling.