QuantTree histograms

Given a training set drawn from an unknown $d$-variate probability distribution, QuantTree constructs a histogram by recursively splitting $\mathbb{R}^d$. The splits are defined by a stochastic process so that each bin contains a certain proportion of the training set. These histograms can be used to define test statistics (e.g., the Pearson statistic) to tell whether a batch of data is drawn from $\phi_0$ or not. The most crucial property of QuantTree is that the distribution of any statistic based on QuantTree histograms is independent of $\phi_0$, thus enabling nonparametric statistical testing.