Bayesian Inference for Partially Identified Models: Exploring the Limits of Limited Data, 1st Edition (Hardback) book cover

Bayesian Inference for Partially Identified Models

Exploring the Limits of Limited Data, 1st Edition

By Paul Gustafson

Chapman and Hall/CRC

196 pages | 45 B/W Illus.

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Hardback: 9781439869390
pub: 2015-04-01
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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.


"… In this little gem of a monograph, Paul Gustafson … argues that partially identified models should not be so quickly dismissed. … Gustafson has drawn together many discussions of identifiability from previous Bayesian analyses (including his own), which are not widely known in non-Bayesian circles. The writing is concise. The examples are simple and insightful. The reader need not be a Bayesian to appreciate this fine monograph."

—Dale J. Poirier, University of California, Irvine, in Journal of the American Statistical Association, January 2017

Table of Contents



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


Concluding Thoughts

What Have Others Said?

What Is the Road ahead?


About the Author

Paul Gustafson is a professor in the Department of Statistics at the University of British Columbia. He is the statistics editor for Epidemiology as well as an associate editor for the Journal of the American Statistical Association (Applications and Case Studies Section) and Statistics in Medicine. His current research focuses on identification issues in Bayesian analysis.

About the Series

Chapman & Hall/CRC Monographs on Statistics and Applied Probability

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Subject Categories

BISAC Subject Codes/Headings:
MATHEMATICS / Probability & Statistics / General
MEDICAL / Epidemiology