  Tree reconstruction methods are often judged by their accuracy, measured by
how close they get to the true tree. Yet most reconstruction methods like ML do
not explicitly maximize this accuracy. To address this problem, we propose a
Bayesian solution. Given tree samples, we propose finding the tree estimate
which is closest on average to the samples. This ``median'' tree is known as
the Bayes estimator (BE). The BE literally maximizes posterior expected
accuracy, measured in terms of closeness (distance) to the true tree. We
discuss a unified framework of BE trees, focusing especially on tree distances
which are expressible as squared euclidean distances. Notable examples include
Robinson--Foulds distance, quartet distance, and squared path difference. Using
simulated data, we show Bayes estimators can be efficiently computed in
practice by hill climbing. We also show that Bayes estimators achieve higher
accuracy, compared to maximum likelihood and neighbor joining.
