  We define a novel class of additive models called Extended Latent Gaussian
Models and develop a fast, scalable approximate Bayesian inference methodology
for this class. The new class covers a wide range of interesting models, and
the new methodology is better suited to large samples than existing approaches.
We discuss convergence theory for our posterior approximations. We then
illustrate the computational aspects of our approach through a comparison to
existing methods, and demonstrate its application in three challenging
examples: the analysis of aggregated spatial point process data, the fitting of
a Cox proportional hazards model with partial likelihood and a latent spatial
point process, and an astrophysical model for estimating the mass of the Milky
Way in the presence of multivariate measurement uncertainties. Computations
make use of the publicly available aghq package in the R language and code for
the examples in the paper is available from
https://github.com/awstringer1/elgm-paper-code
