Gaussian processes (GP) are known for their outstanding smoothing properties and flexibility in modeling complex nonlinear relationships among variables. Recently, they have been utilized in actuarial science to estimate potential insurance claims. However, in insurance practice, claims data often exhibits non-negative support and asymmetry, resulting in significant model errors when the GP model is employed for claim prediction. This paper intends to replace the Gaussian distribution in GP with a log-Gaussian distribution to construct a log-Gaussian process (LGP) model. The properties and training methods of LGP are discussed. Furthermore, the LGP regression model is employed for estimating claims reserve. It is shown that the LGP regression model offers higher prediction accuracy and reliability compared to other models, particularly the GP regression model, making it more suitable for claims reserving.
Lu et al. (Thu,) studied this question.