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

Paul Gustafson

April 1, 2015 by Chapman and Hall/CRC
Reference - 196 Pages - 45 B/W Illustrations
ISBN 9781439869390 - CAT# K13182
Series: Chapman & Hall/CRC Monographs on Statistics & Applied Probability

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  • Explores the past, present, and future research directions of Bayesian inference in partially identified contexts
  • Covers a range of PIMs, including models for misclassified data and models involving instrumental variables
  • Includes real data applications of PIMs that have recently appeared in the literature
  • Addresses issues relevant to epidemiological, ecological, and other studies, including tradeoffs between strong versus weak assumptions as well as how much data is worth collecting


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.