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• W3086546527 abstract "Summary 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 coefficients. In addition to the usual posterior, the fractional posterior, which is obtained by applying Bayes theorem with a fractional power of the likelihood, is also considered. The latter allows uniformity in posterior contraction over a larger subset of the parameter space. In our set-up, the link function of the generalized linear model need not be canonical. We show that Bayesian methods achieve convergence properties analogous to lasso-type procedures. Our results can be used to derive posterior contraction rates in many generalized linear models including logistic, Poisson regression and others." @default.
• W3086546527 created "2020-09-21" @default.
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• W3086546527 date "2020-09-14" @default.
• W3086546527 modified "2023-10-01" @default.
• W3086546527 title "Posterior contraction in sparse generalized linear models" @default.
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• W3086546527 doi "https://doi.org/10.1093/biomet/asaa074" @default.
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