We analyze with the Bayesian method the solar and KamLAND neutrino data in terms of neutrino oscillations. We show that Bayesian credible regions with a flat prior in the tan^2(theta12)--(Delta m^2)_21 plane strongly support the LMA solution, in agreement with the usual chi-square analysis. Other reasonable priors are considered in order to test the stability of the LMA solution. We show that priors which favor small or large values of the mixing angle lead to minor changes of the allowed LMA region, affecting mainly its large tan^2(theta12) part.
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