Bayesian indirect inference for models with intractable normalizing functions. Issue 2 (22nd January 2021)

• Record Type: Journal Article
• Authors: Park, Jaewoo
• Is Part Of: Journal of statistical computation and simulation. Volume 91:Issue 2(2021)
• Page Start: 300
• Page End: 315
• Publication Date: 2021-01-22
• Subjects: Doubly intractable distributions -- exponential random graph models -- summary statistics -- Gaussian processes -- auxiliary variable; 62; Mathematical statistics -- Data processing -- Periodicals; Digital computer simulation -- Periodicals; 519.5028505
• DOI: 10.1080/00949655.2020.1814286
• Languages: English
• ISSNs: 0094-9655

Abstract

Abstract : Inference for doubly intractable distributions is challenging because the intractable normalizing functions of these models include parameters of interest. Previous auxiliary variable MCMC algorithms are infeasible for multi-dimensional models with large data sets because they depend on expensive auxiliary variable simulation. We develop a fast Bayesian indirect algorithm by replacing an expensive auxiliary variable simulation from a probability model with a computationally cheap simulation from a surrogate model. We learn the relationship between the surrogate model parameters and the probability model parameters using Gaussian process approximations. We apply our methods to challenging examples, and illustrate that the algorithm addresses both computational and inferential challenges for doubly intractable distributions. Especially for a large social network model with 10 parameters, we show that our method can reduce computing time from about 2 weeks to 5 hours, compared to the previous method.