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.