  Recently, S. Arlot and R. Genuer have shown that a model of random forests
outperforms its single-tree counterpart in the estimation of $\alpha-$H\"older
functions, $\alpha\leq2$. This backs up the idea that ensembles of tree
estimators are smoother estimators than single trees. On the other hand, most
positive optimality results on Bayesian tree-based methods assume that
$\alpha\leq1$. Naturally, one wonders whether Bayesian counterparts of forest
estimators are optimal on smoother classes, just like it has been observed for
frequentist estimators for $\alpha\leq 2$. We dwell on the problem of density
estimation and introduce an ensemble estimator from the classical (truncated)
P\'olya tree construction in Bayesian nonparametrics. The resulting Bayesian
forest estimator is shown to lead to optimal posterior contraction rates, up to
logarithmic terms, for the Hellinger and $L^1$ distances on probability density
functions on $[0;1)$ for arbitrary H\"older regularity $\alpha>0$. This
improves upon previous results for constructions related to the P\'olya tree
prior whose optimality was only proven in the case $\alpha\leq 1$. Also, we
introduce an adaptive version of this new prior in the sense that it does not
require the knowledge of $\alpha$ to be defined and attain optimality.
