Kriging models are widely employed due to their simplicity and flexibility in a variety of fields. To gain more distributional information about the unknown parameters, we focus on constructing the fiducial distribution of Kriging model parameters. To solve the challenge of constructing the fiducial marginal distribution for the spatially related parameter, we substitute the Bayesian posterior distribution for the fiducial distribution of this spatially related parameter and present a quasi-fiducial distribution for Kriging model parameters. A Gibbs sampling algorithm is given to get the samples of the quasi-fiducial distribution. Then a model selection criterion based on the quasi-fiducial distribution is proposed. Numerical studies demonstrate that the proposed method is superior to the Lasso and Elastic Net.

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To cite this article: Chen Fan, Shuqin Zhang & Xinmin Li (05 Aug 2025): The quasifiducial model selection for Kriging model, Statistical Theory and Related Fields, DOI: 10.1080/24754269.2025.2537484

To link to this article: https://doi.org/10.1080/24754269.2025.2537484