Kernel Selection for Gaussian Process in Cosmology: With Approximate Bayesian Computation Rejection and Nested Sampling

Gaussian Process (GP) has gained much attention in cosmology due to its ability reconstruct cosmological data a model-independent manner. In this study, we compare two methods for GP kernel selection: Approximate Bayesian Computation (ABC) Rejection and nested sampling. We analyze three types of data: cosmic Chronometer (CC), Type Ia Supernovae (SNIa), Gamma Ray Burst (GRB), using five functions. To evaluate the differences between functions, assess strength evidence Bayes factors. Our results show that, ABC Rejection, Mat\'ern with $\nu$=5/2 (M52 kernel) outperformes commonly used Radial Basis Function (RBF) approximating all datasets. factors indicate that M52 typically supports observed better than RBF kernel, but no clear advantage over other alternatives. However, sampling gives different results, losing advantage. Nevertheless, significant dependence on each kernel.