Figure 1.

(Left) Realization of 4 microbial distributions from our dependent Dirichlet processes. We illustrate 10 representative OTUs and set α = 100. The miniature figure at the top-left corner shows the relative positions of the four biological sample vectors Y^j. The OTUs are those associated to the 10 largest σ’s. As suggested by this panel, the larger the angle between two Y^j’s, the more the corresponding random distributions tend to concentrate on distinct sets. (Right) Correlation of two random probability measures when the cosine ϕ(j, j′) between Y^j and ${\mathbf{Y}}^{j\prime }$ varies from −1 to 1. We consider five different values of the concentration parameter α. In the right panel we also mark with crosses the correlations between P^j(A) and ${\mathbf{Y}}^{j\prime }$ (A) for pairs of biological samples j, j′ considered in the left panel.