  We study the posterior contraction behavior of the latent population
structure that arises in admixture models as the amount of data increases. We
adopt the geometric view of admixture models - alternatively known as topic
models - as a data generating mechanism for points randomly sampled from the
interior of a (convex) population polytope, whose extreme points correspond to
the population structure variables of interest. Rates of posterior contraction
are established with respect to Hausdorff metric and a minimum matching
Euclidean metric defined on polytopes. Tools developed include posterior
asymptotics of hierarchical models and arguments from convex geometry.
