CUORE-0 background analysis and evaluation of $^{130}$Te $2\nu\beta\beta$ decay half-life

CUORE is a bolometric experiment that will search for the Neutrinoless Double Beta decay of $^{130}$Te. CUORE-0 is a single CUORE-like tower that was run between 2013 and 2015 to test the performance of the CUORE experiment. In this proceeding we present the results of the model developed to disentangle and quantify the background sources that combine to form the CUORE-0 energy spectrum. We use detailed Geant4-based simulations and a Bayesian fitting algorithm to reconstruct the experimental data and evaluate the activities of the background sources. A direct outcome of this analysis is the measurement of the $^{130}$Te $2\nu\beta\beta$ decay half-life, of which we provide a preliminary evaluation.