  Blazar TXS 0506+056 is the main candidate for a coincident neutrino and
gamma-ray flare event. In this paper, we present a detailed kinetic
lepto-hadronic emission model capable of producing a photon and neutrino
spectrum given a set of parameters. Our model includes a range of large-scale
geometries and both dynamical and steady-state injection models for electrons
and protons. 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. Assuming a fiducial neutrino flux, we
demonstrate how multi-messenger observations can be modelled jointly in a
Bayesian framework. We find the best parameters for each of the variants of the
model tested and report on their cross-correlations. Additionally, we confirm
that reproducing the neutrino flux of TXS 0506+056 requires an extreme proton
to electron ratio either in the local acceleration process or from external
injection.
