Efficient Bayesian multinomial logistic regression based on heavy-tailed (hyper-LASSO, non-convex) priors. The posterior of coefficients and hyper-parameters is sampled with restricted Gibbs sampling for leveraging the high-dimensionality and Hamiltonian Monte Carlo for handling the high-correlation among coefficients. A detailed description of the method: Li and Yao (2018), Journal of Statistical Computation and Simulation, 88:14, 2827-2851, <doi:10.48550/arXiv.1405.3319>.
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