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贝叶斯桥估计AI 解读

Summary We propose the Bayesian bridge estimator for regularized regression and classification. Two key mixture representations for the Bayesian bridge model are developed: a scale mixture of normal distributions with respect to an α-stable random variable; a mixture of Bartlett–Fejer kernels (or triangle densities) with respect to a two-component mixture of gamma random variables. Both lead to Markov chain Monte Carlo methods for posterior simulation, and these methods turn…

利用 Pólya–Gamma 潜变量进行逻辑模型贝叶斯推断AI 解读

We propose a new data-augmentation strategy for fully Bayesian inference in models with binomial likelihoods. The approach appeals to a new class of Pólya–Gamma distributions, which are constructed in detail. A variety of examples are presented to show the versatility of the method, including logistic regression, negative binomial regression, nonlinear mixed-effect models, and spatial models for count data. In each case, our data-augmentation strategy leads to simple,…