Bayesian model selection in additive partial linear models via locally adaptive splines

We consider a model selection problem for additive partial linear models that provide a flexible framework allowing both linear and nonlinear additive components. In practice, it is challenging to determine which additive components should be excluded from the model and simultaneously determine whether nonzero nonlinear components can be further simplified to linear components in the final model. In this paper, we propose a new Bayesian framework for data-driven model selection by conducting careful model specification, including the choice of prior distribution and of nonparametric model for the nonlinear additive components, and propose new sophisticated computational strategies. Our models, methods, and algorithms are deployed on a suite of numerical studies and applied to a nutritional epidemiology study. The numerical results show that the proposed methodology outperforms previously available methodologies in terms of effective sample sizes of the Markov chain samplers and the overall misclassification rates, especially in high-dimensional and large-sample cases.