Diagnostics for Monte Carlo Algorithms for Models with Intractable Normalizing Functions

• Activity Number: 169 - Advanced Bayesian Topics (Part 2)
• Type: Contributed
• Date/Time: Tuesday, August 10, 2021 : 10:00 AM to 11:50 AM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Bokgyeong Kang* and John Hughes and Murali Haran
• Companies: The Pennsylvania State University and The Pennsylvania State University and Pennsylvania State University
• Keywords: Bartlett identity; Convergence diagnostics; Doubly intractable distribution; Importance sampling; Kernel Stein discrepancy; Markov chain Monte Carlo

Abstract

Models with intractable normalizing constants have many applications. Because the normalizing constants are functions of the parameters of interest, standard Markov chain Monte Carlo cannot be used for Bayesian inference. Several algorithms have been developed for such models, some of which are asymptotically inexact. Currently, however, there are no methods to diagnose convergence of these asymptotically inexact algorithms or to compare their performance to other algorithms. Besides, these algorithms can be difficult to tune. We propose two new diagnostics that address these problems. One of our diagnostics, inspired by the second Bartlett identity, applies widely to asymptotically inexact algorithms (not just for models with intractable normalizing functions). We develop an approximate version of this that is applicable to intractable normalizing function problems. Our second diagnostic is a Monte Carlo approximation to a kernel Stein discrepancy-based diagnostic introduced by Gorham and Mackey (2017). We provide theoretical justification for our methods. And we apply our new diagnostics to several algorithms in the context of challenging simulated and real data examples.