2025/07/09 by Seongmin Kim, Kim, Seongmin, Jaewon Oh +7
Computer Science · Mathematics · #Applications (stat.AP) #Bayesian Methods and Mixture Models #FOS: Computer and information sciences #Gaussian Processes and Bayesian Inference #Methodology (stat.ME) #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.2507.06785
openalex publication_date 2025/07/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Missing data is a common issue in various fields such as medicine, social sciences, and natural sciences, and it poses significant challenges for accurate statistical analysis. Although numerous imputation methods have been proposed to address this issue, many of them fail to adequately capture the complex dependency structure among variables. To overcome this limitation, models based on the Gaussian copula framework have been introduced. However, most existing copula-based approaches do not account for the uncertainty in the marginal distributions, which can lead to biased marginal estimates and degraded performance, especially under high missingness rates. In this study, we propose a Bayesian bootstrap-based Gaussian Copula model (BBGC) that explicitly incorporates uncertainty in the marginal distributions of each variable. The proposed BBGC combines the flexible dependency modeling capability of the Gaussian copula with the Bayesian uncertainty quantification of marginal cumulative distribution functions (CDFs) via the Bayesian bootstrap. Furthermore, it is extended to handle mixed data types by incorporating methods for ordinal variable modeling. Through simulation studies and experiments on real-world datasets from the UCI repository, we demonstrate that the proposed BBGC outperforms existing imputation methods across various missing rates and mechanisms (MCAR, MAR). Additionally, the proposed model shows superior performance on real semiconductor manufacturing process data compared to conventional imputation approaches.