—Classification trees have been extensively studied for decades. In the online learning scenario, a whole class of algorithms for decision trees has been introduced, called incremental decision trees. In the case where subtrees may not be discarded, an incremental decision tree can be seen as a sequential decision process, consisting in deciding to extend the existing tree or not. This problem involves an trade-off between exploration and exploitation, which is addressed in recent work with the use of Hoeffding's bounds. This paper proposes to use Bayesian Credible Intervals instead, in order to get the most out of the knowledge of the output's distribution's shape. It also studies the case of Active Learning in such a tree following the Optimism in the Face of Uncertainty paradigm. Two novel algorithms are introduced for the online and active learning problems. Evaluations on real-world datasets show that these algorithms compare positively to state-of-the-art.