Revealing Hidden Structure by Prof. Wenxin Du, The Ohio State

With the growing complexity of data and models, coupled with rapid advancements in computational power, Bayesian statistics have gained significant popularity for its flexibility in incorporating prior knowledge and handling uncertainty. From machine learning to biostatistics, Bayesian approaches offer a powerful framework for modeling intricate systems. However, as these models become more complex, assessing model fit becomes increasingly challenging, sparking interest in the development of novel Bayesian diagnostics.Bayesian statistics has gained significant popularity for its flexibility in incorporating prior knowledge and handling uncertainty. From machine learning to biostatistics, Bayesian approaches offer a powerful framework for modeling intricate systems. However, as these models become more complex, assessing model fit becomes increasingly challenging, sparking interest in the development of novel Bayesian diagnostics.

This talk will introduce the core ideas of Bayesian statistics and diagnostic methods, with an emphasis on a novel approach using case deletion weights (CDWs). CDWs measure the influence of individual data points on model fit and exhibit unique behaviors in the presence of model misspecification. By exploring different aspects of these weights, we can develop intuitive and concise diagnostic methods in the form of graphical summaries and low-dimensional quantitative measures, providing valuable insights into uncovering hidden structures in complex data and aiding in model refinement.