Model Uncertainty and Missing Data: An Objective Bayesian Perspective

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...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2024-10
Main Authors: García-Donato, Gonzalo, Castellanos, María Eugenia, Cabras, Stefano, Quirós, Alicia, te, Anabel
Format: Article
Language:English
Subjects:
Bayesian analysis
Feature selection
Missing data
Regression models
Statistical analysis
Uncertainty
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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. 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.
ISSN:2331-8422