Abstract
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 language | English |
|---|---|
| Pages (from-to) | 1372-1390 |
| Number of pages | 19 |
| Journal | Journal of the American Statistical Association |
| Volume | 113 |
| Issue number | 523 |
| DOIs | |
| Publication status | Published - 2018 Jul 3 |
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All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Statistics, Probability and Uncertainty
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Bayesian Inference in the Presence of Intractable Normalizing Functions. / Park, Jaewoo; Haran, Murali.
In: Journal of the American Statistical Association, Vol. 113, No. 523, 03.07.2018, p. 1372-1390.Research output: Contribution to journal › Review article
TY - JOUR
T1 - Bayesian Inference in the Presence of Intractable Normalizing Functions
AU - Park, Jaewoo
AU - Haran, Murali
PY - 2018/7/3
Y1 - 2018/7/3
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85054626424&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85054626424&partnerID=8YFLogxK
U2 - 10.1080/01621459.2018.1448824
DO - 10.1080/01621459.2018.1448824
M3 - Review article
AN - SCOPUS:85054626424
VL - 113
SP - 1372
EP - 1390
JO - Journal of the American Statistical Association
JF - Journal of the American Statistical Association
SN - 0162-1459
IS - 523
ER -