Algorithms for Models with Intractable Normalizing Functions

Models with intractable normalizing functions arise in a wide variety of areas, from models for networks to models for lattice and spatial point processes, permutations, count data, and gene expression. We describe a number of recent algorithms for such models, providing a framework for understanding them while also showcasing practical implementation issues via several challenging examples. We present diagnostics for assessing the accuracy of approximations produced by these algorithms and show how the diagnostics are particularly valuable for algorithm tuning. Finally we discuss a broader class of algorithms for problems where the entire likelihood is difficult to evaluate but where it is common to be able to simulate from the probability model of interest; this is a fast-growing research area commonly referred to as simulation-based inference.