Convergence analysis of data augmentation algorithms in Bayesian lasso models with log-concave likelihoods
对数凹似然贝叶斯 lasso 模型中数据增广算法的收敛性分析
We study the convergence properties of a class of data augmentation algorithms targeting posterior distributions of Bayesian lasso models with log-concave likelihoods. Leveraging isoperimetric inequalities, we derive a generic convergence bound for this class of algorithms and apply it to Bayesian probit, logistic, and heteroskedastic Gaussian linear lasso models. Under feasible initializations, the mixing times for the probit and logistic models are of order $O[(p+n)^3 (pn^{1-c} + n)]$…