Bayesian Inference in the Presence of Intractable Normalizing Functions

• Activity Number: 302 - Bayesian Modeling
• Type: Contributed
• Date/Time: Tuesday, August 1, 2017 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Computing
• Author(s): Jaewoo Park*
• Companies: Penn State University
• Keywords: Doubly intractable distributions ; Importance sampling ; Gaussian process ; Social network models ; Point process ; Markov Chain Monte Carlo

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 eciency of these algorithms and discuss their theoretical bases. We propose novel algorithms based on the Gaussian process approximations that provide computational gains over existing methods.