A fully Bayesian approach to the generalized hyperbolic process for regression

This study presents a new and flexible approach to regression modeling called the Generalized Hyperbolic Process for Regression (GHPR), which builds on and extends the well-known Gaussian Process for Regression (GPR). The GHPR is designed to cover a broader range of regression behaviors, with GPR appearing as a special case within this wider framework. A fully Bayesian modeling strategy is used to capture uncertainty and improve prediction. Because the model can be computationally demanding, the analysis focuses on a more efficient weight-space version. To model complex relationships in the data, the approach uses Fourier basis functions, and the Laplace approximation is applied to make inference more tractable. The study also includes theoretical results for both the marginal and predictive distributions. To test how well the model performs, simulations under two scenarios are carried out, and both GHPR and GPR are applied to real data on semiconductor electron mobility. The results show that GHPR consistently provides more accurate predictions.