Fast, Scalable Approximations to Posterior Distributions in Extended Latent Gaussian Models

We define a novel class of additive models, called Extended Latent Gaussian Models, that allow for wide range response distributions and flexible relationships between the predictor mean response. The new covers broad interesting models including multi-resolution spatial processes, partial likelihood-based survival multivariate measurement error models. Because computation exact posterior distribution is infeasible, we develop fast, scalable approximate Bayesian inference methodology this based on nested Gaussian, Laplace, adaptive quadrature approximations. prove in these posteriors op(1) under standard conditions, provide numerical evidence suggesting our method runs faster scales to larger datasets than methods Integrated Nested Laplace Approximations Markov chain Monte Carlo, with comparable accuracy. apply mapping malaria incidence rates continuous space using aggregated data, leukemia hazards Cox Proportional-Hazards model continuously-varying process, estimating mass Milky Way Galaxy noisy measurements positions velocities star clusters its orbit. Supplementary materials article are available online.