Implementing Approximate Bayesian Inference using Adaptive Quadrature: the aghq Package

TL;DR

The paper introduces the aghq package for efficient approximate Bayesian inference using adaptive quadrature, demonstrating its application across diverse complex models with minimal additional coding.

Contribution

It presents a new software package that simplifies and extends Bayesian inference capabilities in challenging models, especially when integrated with TMB.

Findings

Successfully applied to infectious disease models

Estimated Milky Way mass using astrostatistical models

Handled zero-inflation and overdispersion in count data

Abstract

The aghq package for implementing approximate Bayesian inference using adaptive quadrature is introduced. The method and software are described, and use of the package in making approximate Bayesian inferences in several challenging low- and high-dimensional models is illustrated. Examples include an infectious disease model; an astrostatistical model for estimating the mass of the Milky Way; two examples in non-Gaussian model-based geostatistics including one incorporating zero-inflation which is not easily fit using other methods; and a model for zero-inflated, overdispersed count data. The aghq package is especially compatible with the popular TMB interface for automatic differentiation and Laplace approximation, and existing users of that software can make approximate Bayesian inferences with aghq using very little additional code. The aghq package is available from CRAN and complete code for all examples in this paper can be found at https://github.com/awstringer1/aghq-software-paper-code.