Curve Fitting Algorithm of Functional Radiation-Response Data Using Bayesian Hierarchical Gaussian Process Regression Model

We present a nonparametric Bayesian hierarchical (NBH) model and develop a variational approximation (VA) algorithm for the curve fitting of the functional radiation response data. The NBH model is based on a Bayesian hierarchical (BH) model with a Gaussian-Inverse Wishart process (G-IWP) prior, which simultaneously smooths multiple functional observations and estimates mean-covariance functions. We use the automatic differentiation variational inference (ADVI) algorithm with a Gaussian distribution as the variational distribution for approximating the posterior distribution of parameters of interest, which is applicable to a wide class of probabilistic models and can also be implemented in Stan (a probabilistic programming system). Using the NBH model and the Gaussian ADVI algorithm, we fit a dataset for the semiconductor obtained from the radiation response map (RRM) of South Korea.