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February 2015 Posterior contraction of the population polytope in finite admixture models
XuanLong Nguyen
Bernoulli 21(1): 618-646 (February 2015). DOI: 10.3150/13-BEJ582


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.


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XuanLong Nguyen. "Posterior contraction of the population polytope in finite admixture models." Bernoulli 21 (1) 618 - 646, February 2015.


Published: February 2015
First available in Project Euclid: 17 March 2015

zbMATH: 1368.62288
MathSciNet: MR3322333
Digital Object Identifier: 10.3150/13-BEJ582

Rights: Copyright © 2015 Bernoulli Society for Mathematical Statistics and Probability


Vol.21 • No. 1 • February 2015
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