Blazar TXS 0506+056 is the main candidate for a coincident neutrino and gamma-ray flare event. In this paper, we compose a detailed lepto-hadronic emission model capable of producing a photon and neutrino spectrum given a set of parameters. We link this model with a Markov Chain Monte Carlo sampler to obtain a powerful statistical tool that allows us to both fit the Spectral Energy Distribution and study the probability density functions and correlations of the parameters. We find the best parameters for each of the variants of the model tested and study their correlations. Additionaly, we confirm that reproducing the neutrino flux of TXS 0506+056 requires an extreme proton to electron ratio.