Accelerated Bayesian Kernel Machine Regression: A Gaussian Variational Approximation with the Horseshoe Prior

초록

Bayesian kernel machine regression (BKMR) has emerged as a state-of-the-art method for analyzing the effects of multiple exposures in environmental epidemiology. However, its use has been limited by the slow convergence of the Markov chain Monte Carlo algorithm. To expand its applicability and include a broader range of models, we propose a new BKMR model with a continuous shrinkage prior and develop a Gaussian variational Bayes method for computing the posterior distribution of parameters of interest. BKMR with random intercepts and slopes is considered as a special case. We also extend a Bayesian multiple index model to incorporate these new features. Our numerical study demonstrates that the proposed method considerably enhances the computational speed without sacrificing accuracy.

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