Implementing Adaptive Quadrature for Bayesian Inference: the aghq Package

I introduce the aghq package for implementing Bayesian inference using adaptive Gauss-Hermite quadrature. I describe the method and software, and illustrate its use in several challenging low- and high-dimensional examples. Specifically, I show how the aghq package can be used as a basis for implementing more complicated inference methods with a focus on aproximate Bayesian inference for Extended Latent Gaussian Models, with two difficult applications in non-Gaussian geostatistical modelling. I also show how the package can be used to make fully Bayesian inferences in models currently fit using frequentist inference by leveraging code from other packages, with an application to a zero-inflated, overdispersed Poisson regression fit using the glmmTMB package.