Dissertation, Otto-Friedrich-Universität Bamberg, 2026

This dissertation addresses the challenges of model and variable selection in statistical analysis, with a particular focus on datasets with missing values. Adopting a Bayesian framework, it introduces an automated approach that explicitly accounts for uncertainty due to missing data while enabling robust selection of relevant variables. The core methodology integrates data augmentation and Markov Chain Monte Carlo (MCMC) techniques to jointly estimate the posterior distributions of parameters and missing values.
The work bridges theoretical foundations of Bayesian inference with practical applications, including the use of spike-and-slab priors for variable selection and the analysis of binary regression models with missing covariates. Empirical studies and simulations demonstrate the superiority of this approach over classical methods such as multiple imputation or shrinkage estimators (e.g., Lasso, Ridge, Elastic Net). The results indicate that the Bayesian approach not only enhances estimation accuracy but also improves model interpretability; especially in high-dimensional and high-missingness scenarios.
A key contribution of this work is its systematic approach to model selection, which relies on Bayes factors, marginal likelihoods, and information criteria (e.g., BIC) to compare competing models, even in the presence of incomplete data. These methods identify the model that strikes the optimal balance between fit and complexity, while model averaging and hierarchical priors ensure stability across different missingness mechanisms (MCAR, MAR, MNAR).
This dissertation contributes to statistical methodology by providing a coherent and flexible solution for the simultaneous handling of missing values, variable selection, and model comparison. It emphasizes the importance of accounting for uncertainty in data analysis and offers practical guidelines for implementation in empirical research.