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We present the Bayesian method for evaluating the evidence for a non-zerovalue of the leptonic mixing angle theta_13 and CP-violation in neutrinooscillation experiments. This is an application of the well-established methodof Bayesian model selection, of which we give a concise and pedagogicaloverview. When comparing the hypothesis theta_13 = 0 with hypotheses wheretheta_13 > 0 using global data but excluding the recent reactor measurements,we obtain only a weak preference for a non-zero theta_13, even though thesignificance is over 3 sigma. We then add the reactor measurements one by oneand show how the evidence for theta_13 > 0 quickly increases. When includingthe Double Chooz, Daya Bay, and RENO data, the evidence becomes overwhelmingwith a posterior probability of the hypothesis theta_13 = 0 below 10^-11 .Owing to the small amount of information on the CP-phase delta, very similarevidences are obtained for the CP-conserving and CP-violating hypotheses.Hence, there is, not unexpectedly, neither evidence for nor against leptonicCP-violation. However, when future experiments aiming to search forCP-violation have started taking data, this question will be of greatimportance and the method described here can be used as an important complementto standard analyses.

Bayesian evidence for non-zero theta_13 and CP-violation in neutrino oscillations