In this paper, we develop a simulation-based framework for regularizedlogistic regression, exploiting two novel results for scale mixtures ofnormals. By carefully choosing a hierarchical model for the likelihood by onetype of mixture, and implementing regularization with another, we obtain newMCMC schemes with varying efficiency depending on the data type (binary v.binomial, say) and the desired estimator (maximum likelihood, maximum aposteriori, posterior mean). Advantages of our omnibus approach includeflexibility, computational efficiency, applicability in p >> n settings,uncertainty estimates, variable selection, and assessing the optimal degree ofregularization. We compare our methodology to modern alternatives on bothsynthetic and real data. An R package called reglogit is available on CRAN.
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