Bayesian Inference for Partially Identified Models: Exploring the Limits of Limited Data shows how the Bayesian approach to inference is applicable to partially identified models (PIMs) and examines the performance of Bayesian procedures in partially identified contexts. Drawing on his many years of research in this area, the author presents a thorough overview of the statistical theory, properties, and applications of PIMs. The book first describes how reparameterization can assist in computing posterior quantities and providing insight into the properties of Bayesian estimators. It next compares partial identification and model misspecification, discussing which is the lesser of the two evils. The author then works through PIM examples in depth, examining the ramifications of partial identification in terms of how inferences change and the extent to which they sharpen as more data accumulate. He also explains how to characterize the value of information obtained from data in a partially identified context and explores some recent applications of PIMs. In the final chapter, the author shares his thoughts on the past and present state of research on partial identification. This book helps readers understand how to use Bayesian methods for analyzing PIMs. Readers will recognize under what circumstances a posterior distribution on a target parameter will be usefully narrow versus uselessly wide.
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
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