Exact O(n^{2}) dynamic programs compute the marginal likelihood and closed-form Beta-mixture posterior of mixture weights under Beta/Beta-Liouville priors, with calibrated intervals in the small-sample regime.
Estimation of a Two-component Mixture Model with Applications to Multiple Testing
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abstract
We consider a two-component mixture model with one known component. We develop methods for estimating the mixing proportion and the unknown distribution nonparametrically, given i.i.d.~data from the mixture model, using ideas from shape restricted function estimation. We establish the consistency of our estimators. We find the rate of convergence and asymptotic limit of the estimator for the mixing proportion. Completely automated distribution-free honest finite sample lower confidence bounds are developed for the mixing proportion. Connection to the problem of multiple testing is discussed. The identifiability of the model, and the estimation of the density of the unknown distribution are also addressed. We compare the proposed estimators, which are easily implementable, with some of the existing procedures through simulation studies and analyse two data sets, one arising from an application in astronomy and the other from a microarray experiment.
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Exact computation of posterior distribution of mixture weights in hierarchical Bayesian models
Exact O(n^{2}) dynamic programs compute the marginal likelihood and closed-form Beta-mixture posterior of mixture weights under Beta/Beta-Liouville priors, with calibrated intervals in the small-sample regime.