Implementing Approximate Bayesian Inference using Adaptive Quadrature: the aghq Package

I introduce the aghq package for implementing approximate 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 considered by Bilodeau et. al. (2021) and others. Specifically, I show how the aghq package is used as a basis for implementing more complicated approximate Bayesian inference methods 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.