Bayesian Indirect Inference for Models with Intractable Normalizing Functions

TL;DR

This paper introduces a fast Bayesian indirect inference method that uses surrogate models and Gaussian process approximations to efficiently perform inference on complex doubly intractable distributions, significantly reducing computation time.

Contribution

The authors develop a novel Bayesian indirect inference algorithm that replaces expensive auxiliary variable simulations with surrogate models, enabling scalable inference for complex models.

Findings

Reduces computation time from 2 weeks to 5 hours for a large social network model.

Addresses both computational and inferential challenges in doubly intractable distributions.

Successfully applied to simulated and real data examples.

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 at each iteration. 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 simulated and real data 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. Our method allows practitioners to carry out Bayesian inference for more complex models with larger data sets than before.