Bayesian indirect inference for models with intractable normalizing functions

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.

Keywords:

• Doubly intractable distributions
• exponential random graph models
• summary statistics
• Gaussian processes
• auxiliary variable

2010 Mathematics Subject Classification:

• 62

Acknowledgments

Jaewoo Park was partially supported by the Yonsei University Research Fund of 2019- 22-0194 and the National Research Foundation of Korea (NRF-2020R1C1C1A0100386811). The author is grateful to the anonymous reviewers for their careful reading and valu- able comments.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

Jaewoo Park was partially supported by the Yonsei University Research Fund of 2019- 22-0194 and the National Research Foundation of Korea (NRF-2020R1C1C1A0100386811).