A Framework for Robust Bayesian Models Under Data Contamination

Thesis Abstract

Data contamination poses a significant challenge to the reliability and robustness of Bayesian models, particularly in real-world contexts where measurement errors, outliers, and incomplete data are prevalent. This study aims to develop a comprehensive framework for constructing and validating robust Bayesian models that maintain statistical integrity under various data contamination scenarios. The specific objectives include identifying key vulnerabilities of traditional Bayesian approaches to contaminated data, evolving a set of robust prior distributions and likelihood specifications, and empirically validating the proposed framework through simulation studies and real-data applications. The research adopts a mixed-methods design, integrating theoretical model development with extensive simulation experiments. The population of the study comprises Bayesian models utilized in applied statistics, machine learning, and data science, with a focus on regression, hierarchical modeling, and classification contexts. A purposive sampling strategy was employed to select representative models and contamination types. Data collection involved generating synthetic datasets under controlled contamination conditions—such as additive outliers, misclassification, and noisy measurements—each comprising at least 1,000 data points across multiple contamination levels. Additionally, real-world datasets from healthcare, finance, and environmental monitoring were incorporated to assess the models' applicability in practical settings. In terms of analysis, the study employs a combination of analytical techniques, including Markov Chain Monte Carlo (MCMC) simulations for posterior estimation, sensitivity analyses to evaluate robustness against varying contamination levels, and model comparison metrics such as the Deviance Information Criterion (DIC) and predictive accuracy measures. The theoretical component involved extending existing robust Bayesian methods, such as contamination models and objective Bayesian priors, within a unified framework. The framework incorporates a novel set of influence-function-based diagnostics and adaptive prior adjustments designed to enhance robustness without compromising efficiency. The methodology also entailed rigorous validation via cross-validation, bootstrap resampling, and convergence diagnostics to ensure model stability and reproducibility. Expected findings suggest that the proposed robust Bayesian framework significantly mitigates the adverse effects of data contamination, resulting in more reliable parameter estimates and superior predictive performance compared to conventional Bayesian models. It is anticipated that models embedded within this framework will display resilience across diverse contamination scenarios, including heavy-tailed noise distributions and systematic outliers. The framework also aims to provide practitioners with a set of diagnostic tools and guidelines for model specification under uncertain data quality conditions. This study contributes to the existing body of knowledge by formalizing a versatile, scalable framework that integrates theoretical robustness principles with practical modeling strategies tailored for contaminated data environments. It extends current Bayesian robustness literature by offering a cohesive approach grounded in influence functions and adaptive priors, thereby filling gaps related to applicability and ease of implementation in complex modeling contexts. The research outcomes are expected to foster more reliable inference in applied statistics, machine learning, and data-driven decision-making processes where data integrity cannot always be guaranteed. The main conclusion underscores the critical importance of incorporating robustness considerations into Bayesian modeling practice, especially in high-stakes domains impacted by data imperfections. Based on the findings, comprehensive recommendations include adopting the developed framework in standard Bayesian workflows, further enhancing influence-function-based diagnostics, and encouraging ongoing research into adaptive prior strategies. Future studies should explore the extension of this framework to high-dimensional data, real-time analytics, and the integration with other robust inferential paradigms to ensure continued advancement in statistical robustness amidst evolving data challenges.