A sparse empirical Bayes approach to high-dimensional Gaussian process-based varying coefficient models

Despite the increasing importance of high-dimensional varying coefficient models, the study of their Bayesian versions is still in its infancy. This paper contributes to the literature by developing a sparse empirical Bayes formulation that addresses the problem of high-dimensional model selection in the framework of Bayesian varying coefficient modelling under Gaussian process (GP) priors. To break the computational bottleneck of GP-based varying coefficient modelling, we introduce the low-cost computation strategy that incorporates linear algebra techniques and the Laplace approximation into the evaluation of the high-dimensional posterior model distribution. A simulation study is conducted to demonstrate the superiority of the proposed Bayesian method compared to an existing high-dimensional varying coefficient modelling approach. In addition, its applicability to real data analysis is illustrated using yeast cell cycle data.