This report tends to provide details on how to perform predictions using Gaussian process regression (GPR) modeling. In this case, we represent proofs for prediction using non-parametric GPR modeling for noise-free predictions as well as prediction using semi-parametric GPR for noisy observations.
Shekaramiz, Mohammad; Moon, Todd K.; and Gunther, Jacob H., "Details on Gaussian Process Regression (GPR) and Semi-GPR Modeling" (2018). Electrical and Computer Engineering Faculty Publications. Paper 216.