# Posterior consistency in linear models under shrinkage priors

@article{Armagan2013PosteriorCI,
title={Posterior consistency in linear models under shrinkage priors},
author={Artin Armagan and David B. Dunson and Jaeyong Lee and Waheed Uz Zaman Bajwa and Nate Strawn},
journal={Biometrika},
year={2013},
volume={100},
pages={1011-1018}
}
We investigate the asymptotic behaviour of posterior distributions of regression coefficients in high-dimensional linear models as the number of dimensions grows with the number of observations. We show that the posterior distribution concentrates in neighbourhoods of the true parameter under simple sufficient conditions. These conditions hold under popular shrinkage priors given some sparsity assumptions. Copyright 2013, Oxford University Press.
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