Posterior contraction in sparse generalized linear models
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DOI: 10.1093/biomet/asaa074
Abstract: We study posterior contraction rates in sparse high-dimensional generalized linear models using priors incorporating sparsity. A mixture of a point mass at zero and a continuous distribution is used as the prior distribution on regression… read more here.
Keywords: contraction sparse; generalized linear; sparse generalized; posterior contraction ... See more keywords
Oracle posterior contraction rates under hierarchical priors
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DOI: 10.1214/21-ejs1811
Abstract: We offer a general Bayes theoretic framework to derive posterior contraction rates under a hierarchical prior design: the first-step prior serves to assess the model selection uncertainty, and the second-step prior quantifies the prior belief… read more here.
Keywords: contraction rates; rates hierarchical; step; posterior contraction ... See more keywords
Posterior contraction and credible regions for level sets
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DOI: 10.1214/21-ejs1846
Abstract: For a given function f on a multivariate domain, the level sets, given by {x:f(x)=c} for different values of c, provide important geometrical insights about the underlying function of interest. The distance on level sets… read more here.
Keywords: level sets; contraction rates; posterior contraction; contraction ... See more keywords