Model uncertainty and missing data: an objective bayesian perspective (with discussion)

The interplay between missing data and model uncertainty—two classic statistical problems—leads to primary questions that we formally address from an objective Bayesian perspective. For the general regression problem, we discuss the probabilistic justification of Rubin’s rules applied to the usual c...

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Detalles Bibliográficos
Autores: García-Donato Layron, Gonzalo, Castellanos , Maria Eugenia, Cabras , Stefano, Quirós , Alicia, Forte , Anabel
Tipo de recurso: artículo
Fecha de publicación:2025
País:España
Institución:Universidad de Castilla-La Mancha
Repositorio:RUIdeRA. Repositorio Institucional de la UCLM
OAI Identifier:oai:ruidera.uclm.es:10578/46154
Acceso en línea:https://hdl.handle.net/10578/46154
Access Level:acceso abierto
Palabra clave:Bayes factor
G-priors
Ignorability
Objective prior distribution
Rubin’s rules
Descripción
Sumario:The interplay between missing data and model uncertainty—two classic statistical problems—leads to primary questions that we formally address from an objective Bayesian perspective. For the general regression problem, we discuss the probabilistic justification of Rubin’s rules applied to the usual components of Bayesian variable selection, arguing that prior predictive marginals should be central to the pursued methodology. In the regression settings, we explore the conditions of prior distributions that make the missing data mechanism ignorable, provided that it is missing at random or completely at random. Moreover, when comparing multiple linear models, we provide a complete methodology for dealing with special cases, such as variable selection or uncertainty regarding model errors. In numerous simulation experiments, we demonstrate that our method outperforms or equals others, in consistently producing results close to those obtained using the full dataset. In general, the difference increases with the percentage of missing data and the correlation between the variables used for imputation. Finally, we summarize possible directions for future research.