Inferring Semi-Parametric Gaussian Process Model Parameters for Missing Geotechnical Data Prediction

Data points in geotechnical site investigation data (i.e., CPT data) may be missing sometimes due to various reasons. This study proposed to use a semi-parametric Gaussian process regression (GPR) method for predicting missing data in geotechnical testing results. Semi-parametric GPR divides the spatial data into the trend function, spatial residual, and measurement errors. Compared with conventional GPR method, semi-parametric GPR enhances model interpretability and accuracy. However, this involves challenges in estimating the parameters in the model. Conventional GPR applications infer the model parameters based on maximum a posteriori (MAP) estimation. However, this method can only provide a point estimation of the model parameters. Point estimation may be trapped by a local optimum result. This study utilizes the Hamiltonian Monte Carlo (HMC) method to get the full posterior distribution of the model parameters. MAP and HMC methods are both applied to infer the model parameters based on a synthetic CPT data set. The performances of both methods are compared with the true model values. The results show that the model parameters estimated from the HMC are more reliable.