Dissertation Defense: Wenxin Du

March 27, 2025

8:00AM - 9:00AM

CH 440

Add to Calendar 2025-03-27 08:00:00 2025-03-27 09:00:00 Dissertation Defense: Wenxin Du Dissertation Defense: Wenxin Du, Statistics Ph.D. CandidateTitle: A Unified Bayesian Model Diagnostic Framework via Case Deletion WeightsAbstract: As Bayesian models become increasingly flexible and high-dimensional, there is a growing need for precise diagnostic tools. A variety of methods exist—some focus on formal model comparison, while others assess whether the posterior predictive distribution can generate data that look like the observed sample. However, these methods often fail to clarify why certain data points heavily influence the posterior or to indicate precisely where assumptions may break down.This thesis introduces a unified, case-deletion-based diagnostic framework centered on case deletion weights (CDWs). By quantifying how removing individual observations shifts the posterior distribution, CDWs link local influence measures to global model assessment. The thesis establishes theoretical guarantees, demonstrating that under model misspecification, posterior average log-CDWs exhibit distinct asymptotic behavior compared to the correctly specified setting. Through simulations and comparisons with established methods—including WAIC, LPML, and LOO-CV—CDW-based metrics are shown to match or surpass standard approaches for Bayesian model comparison across a variety of scenarios (e.g., thick-tailed distributions, omitted predictors, under- or over-specified mixtures). Additionally, the thesis proposes a new posterior predictive approach leveraging the average log-CDW to evaluate model performance in isolation. A further contribution is the analysis of the variance-covariance matrix of log-CDWs, which reveals how pairs of observations jointly influence inferences. In particular, systematic model misfit manifests as unique block structures within these matrices. Visualizing these correlations can help uncover missing mixture components or other structural gaps, thereby providing a pathway for iterative model refinement.By connecting principled asymptotic theory with practical diagnostics, this work establishes a comprehensive Bayesian model assessment framework that unifies model comparison, standalone model evaluation, and rigorous model diagnostics.Advisor: Mario Peruggia CH 440 OSU ASC Drupal 8 ascwebservices@osu.edu America/New_York public

2025-03-27 08:00:00 2025-03-27 09:00:00 Dissertation Defense: Wenxin Du Dissertation Defense: Wenxin Du, Statistics Ph.D. CandidateTitle: A Unified Bayesian Model Diagnostic Framework via Case Deletion WeightsAbstract: As Bayesian models become increasingly flexible and high-dimensional, there is a growing need for precise diagnostic tools. A variety of methods exist—some focus on formal model comparison, while others assess whether the posterior predictive distribution can generate data that look like the observed sample. However, these methods often fail to clarify why certain data points heavily influence the posterior or to indicate precisely where assumptions may break down.This thesis introduces a unified, case-deletion-based diagnostic framework centered on case deletion weights (CDWs). By quantifying how removing individual observations shifts the posterior distribution, CDWs link local influence measures to global model assessment. The thesis establishes theoretical guarantees, demonstrating that under model misspecification, posterior average log-CDWs exhibit distinct asymptotic behavior compared to the correctly specified setting. Through simulations and comparisons with established methods—including WAIC, LPML, and LOO-CV—CDW-based metrics are shown to match or surpass standard approaches for Bayesian model comparison across a variety of scenarios (e.g., thick-tailed distributions, omitted predictors, under- or over-specified mixtures). Additionally, the thesis proposes a new posterior predictive approach leveraging the average log-CDW to evaluate model performance in isolation. A further contribution is the analysis of the variance-covariance matrix of log-CDWs, which reveals how pairs of observations jointly influence inferences. In particular, systematic model misfit manifests as unique block structures within these matrices. Visualizing these correlations can help uncover missing mixture components or other structural gaps, thereby providing a pathway for iterative model refinement.By connecting principled asymptotic theory with practical diagnostics, this work establishes a comprehensive Bayesian model assessment framework that unifies model comparison, standalone model evaluation, and rigorous model diagnostics.Advisor: Mario Peruggia CH 440 America/New_York public

Dissertation Defense: Wenxin Du, Statistics Ph.D. Candidate

Title: A Unified Bayesian Model Diagnostic Framework via Case Deletion Weights

Abstract: As Bayesian models become increasingly flexible and high-dimensional, there is a growing need for precise diagnostic tools. A variety of methods exist—some focus on formal model comparison, while others assess whether the posterior predictive distribution can generate data that look like the observed sample. However, these methods often fail to clarify why certain data points heavily influence the posterior or to indicate precisely where assumptions may break down.

This thesis introduces a unified, case-deletion-based diagnostic framework centered on case deletion weights (CDWs). By quantifying how removing individual observations shifts the posterior distribution, CDWs link local influence measures to global model assessment. The thesis establishes theoretical guarantees, demonstrating that under model misspecification, posterior average log-CDWs exhibit distinct asymptotic behavior compared to the correctly specified setting. Through simulations and comparisons with established methods—including WAIC, LPML, and LOO-CV—CDW-based metrics are shown to match or surpass standard approaches for Bayesian model comparison across a variety of scenarios (e.g., thick-tailed distributions, omitted predictors, under- or over-specified mixtures). Additionally, the thesis proposes a new posterior predictive approach leveraging the average log-CDW to evaluate model performance in isolation. A further contribution is the analysis of the variance-covariance matrix of log-CDWs, which reveals how pairs of observations jointly influence inferences. In particular, systematic model misfit manifests as unique block structures within these matrices. Visualizing these correlations can help uncover missing mixture components or other structural gaps, thereby providing a pathway for iterative model refinement.

By connecting principled asymptotic theory with practical diagnostics, this work establishes a comprehensive Bayesian model assessment framework that unifies model comparison, standalone model evaluation, and rigorous model diagnostics.

Advisor: Mario Peruggia