# Bayesian Inference in the Presence of Intractable Normalizing Functions

## TL;DR

This paper reviews and compares Monte Carlo algorithms for Bayesian inference in models with intractable normalizing functions, highlighting their efficiency and theoretical foundations through simulations and real data examples.

## Contribution

It provides a unifying framework for understanding existing algorithms and offers practical recommendations for their application in complex statistical models.

## Key findings

- Different algorithms vary in computational efficiency
- Connections among algorithms are clarified
- Guidelines for practitioners are provided

## 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 efficiency of these algorithms and discuss their theoretical bases. Our study provides practical recommendations for practitioners along with directions for future research for MCMC methodologists.