Bayesian Inference for Partially Identified Models: Exploring the Limits of Limited Data

TLDR: In this article, the authors discuss the importance of partial identification in Partially Identified Models (PIMs) and their relationship with Bayesian Inference and Model Misspecification.

Abstract: Introduction Identification What Is against Us? What Is for Us? Some Simple Examples of Partially Identified Models The Road Ahead The Structure of Inference in Partially Identified Models Bayesian Inference The Structure of Posterior Distributions in PIMs Computational Strategies Strength of Bayesian Updating, Revisited Posterior Moments Credible Intervals Evaluating the Worth of Inference Partial Identification versus Model Misspecification The Siren Call of Identification Comparing Bias Reflecting Uncertainty A Further Example Other Investigations of PIM versus IPMM Models Involving Misclassification Binary to Trinary Misclassification Binary Misclassification across Three Populations Models Involving Instrumental Variables What Is an Instrumental Variable? Imperfect Compliance Modeling an Approximate Instrumental Variable Further Examples Inference in the Face of a Hidden Subpopulation Ecological Inference, Revisited Further Topics Computational Considerations Study Design Considerations Applications Concluding Thoughts What Have Others Said? What Is the Road ahead? Index