Bayesian Inference in the Presence of Intractable Normalizing Functions

Jaewoo Park, Murali Haran

Research output: Contribution to journalReview articlepeer-review

32 Citations (Scopus)


Models with intractable normalizing functions arise frequently in statistics. Common examples of such models include exponential random graph models for social networks and Markov point processes for ecology and disease modeling. Inference for these models is complicated because the normalizing functions of their probability distributions include the parameters of interest. In Bayesian analysis, they result in so-called doubly intractable posterior distributions which pose significant computational challenges. Several Monte Carlo methods have emerged in recent years to address Bayesian inference for such models. We provide a framework for understanding the algorithms, and elucidate connections among them. Through multiple simulated and real data examples, we compare and contrast the computational and statistical efficiency of these algorithms and discuss their theoretical bases. Our study provides practical recommendations for practitioners along with directions for future research for Markov chain Monte Carlo (MCMC) methodologists. Supplementary materials for this article are available online.

Original languageEnglish
Pages (from-to)1372-1390
Number of pages19
JournalJournal of the American Statistical Association
Issue number523
Publication statusPublished - 2018 Jul 3

Bibliographical note

Publisher Copyright:
© 2018, © 2018 American Statistical Association.

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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