Posterior contraction of the population polytope in finite admixture models
Abstract
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.
 Publication:

arXiv eprints
 Pub Date:
 May 2012
 arXiv:
 arXiv:1206.0068
 Bibcode:
 2012arXiv1206.0068N
 Keywords:

 Mathematics  Statistics Theory;
 Computer Science  Machine Learning
 EPrint:
 Published at http://dx.doi.org/10.3150/13BEJ582 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)