Invited Discussion of "Model Uncertainty and Missing Data: An Objective Bayesian Perspective" by Gonzalo García-Donato , María Eugenia Castellanos , Stefano Cabras Alicia Quirós , and Anabel Forte
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866918229655420928 |
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| author | Clyde, Merlise A |
| author_facet | Clyde, Merlise A |
| contents | The article by Garc{í}a-Donato and co-authors addresses the dual challenges of accounting for model uncertainty and missing data within the Gaussian regression frameworks from an objective Bayesian perspective. Thru the use of an imputation $g$-prior that replaces $X_γ^TX_γ$ for model $γ$ in the covariance of $β_γ$ with $Σ_{X_γ}$, the authors develop a coherent approach to addressing the missing data problem and model uncertainty simultaneously with random $X_γ$ in the missing at random (MAR) or missing completely at random (MCAR) settings, while still being computationally tractable. I discuss the connection of the imputation $g$-prior to the $g$-prior with imputed $X$, and to model selection for graphical models that provide an alternative justification for the $g$-prior for random $X$s. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_03266 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Invited Discussion of "Model Uncertainty and Missing Data: An Objective Bayesian Perspective" by Gonzalo García-Donato , María Eugenia Castellanos , Stefano Cabras Alicia Quirós , and Anabel Forte Clyde, Merlise A Methodology Statistics Theory Other Statistics The article by Garc{í}a-Donato and co-authors addresses the dual challenges of accounting for model uncertainty and missing data within the Gaussian regression frameworks from an objective Bayesian perspective. Thru the use of an imputation $g$-prior that replaces $X_γ^TX_γ$ for model $γ$ in the covariance of $β_γ$ with $Σ_{X_γ}$, the authors develop a coherent approach to addressing the missing data problem and model uncertainty simultaneously with random $X_γ$ in the missing at random (MAR) or missing completely at random (MCAR) settings, while still being computationally tractable. I discuss the connection of the imputation $g$-prior to the $g$-prior with imputed $X$, and to model selection for graphical models that provide an alternative justification for the $g$-prior for random $X$s. |
| title | Invited Discussion of "Model Uncertainty and Missing Data: An Objective Bayesian Perspective" by Gonzalo García-Donato , María Eugenia Castellanos , Stefano Cabras Alicia Quirós , and Anabel Forte |
| topic | Methodology Statistics Theory Other Statistics |
| url | https://arxiv.org/abs/2512.03266 |