Weakness: The main idea of the paper is not original. The entire Section 2.1 is classical results in Gaussian process modeling. There are many papers and books described it. I only point out one such source, Chapter 3 and 4 of Santner, Thomas J., Brian J. Williams, and William I. Notz. The design and analysis of computer experiments. Springer Science & Business Media, 2013. The proposed Bayes-Sard framework (Theorem 2.7), which I suspected already exist in the Monte Carlo community, is a trivial application of the Gaussian process model in the numerical integration approximation. The convergence results, Theorem 2.11 and Theorem 2.12, are also some trivial extension of the classic results of RKHS methods. See Theorem 11.11 and 11.13 of Wendland, Holger. Scattered data approximation. Vol. 17. Cambridge university press, 2004. Or Theorem 14.5 of Fasshauer, Gregory E. Meshfree approximation methods with MATLAB. Vol. 6. World Scientific, 2007. Quality of this paper is relatively low, even though the clarity of the technical part is good. This work lacks basic originality, as I pointed out in its weakness. Overall, this paper has little significance.
17. Cambridge university press, 2004. Or Theorem 14.5 of Fasshauer, Gregory E. Meshfree approximation methods with MATLAB. Vol.