A kernel-based mixed effect regression model for earthquake ground motions

This paper presents a semi-parametric mixed-effect regression approach for analyzing and modeling earthquake ground motions, taking into account the correlations between records. Using kernels, the proposed method extends the classical mixed model equations to complicated relationships. The predictive equation is composed of parametric and nonparametric parts. The parametric part incorporates known relationships into the model, while the nonparametric part captures the relationships which cannot be cast into a simple parametric form. A least squares kernel machine is used to infer the nonparametric part of the model. The resulting semi-parametric model combines the strengths of parametric and nonparametric approaches, allowing incorporation of prior, well-justified knowledge into the model while retaining flexibility with respect to the explanatory variables for which the functional form is uncertain. Equations for pointwise confidence and prediction intervals around the conditional mean are provided. The validity of the proposed method is demonstrated through numerical simulations and using recorded ground motions.