Improving the INLA approach for approximate Bayesian inference for latent Gaussian models

We introduce a new copula-based correction for generalized linear mixed models (GLMMs) within the integrated nested Laplace approximation (INLA) approach for approximate Bayesian inference for latent Gaussian models. While INLA is usually very accurate, some (rather extreme) cases of GLMMs with e.g. binomial or Poisson data have been seen to be problematic. Inaccuracies can occur when there is a very low degree of smoothing or "borrowing strength" within the model, and we have therefore developed a correction aiming to push the boundaries of the applicability of INLA. Our new correction has been implemented as part of the R-INLA package, and adds only negligible computational cost. Empirical evaluations on both real and simulated data indicate that the method works well

A note on intrinsic Conditional Autoregressive models for disconnected graphs

In this note we discuss (Gaussian) intrinsic conditional autoregressive (CAR) models for disconnected graphs, with the aim of providing practical guidelines for how these models should be defined, scaled and implemented. We show how these suggestions can be implemented in two examples on disease mapping.Comment: 14 page

A spliced Gamma-Generalized Pareto model for short-term extreme wind speed probabilistic forecasting

Renewable sources of energy such as wind power have become a sustainable alternative to fossil fuel-based energy. However, the uncertainty and fluctuation of the wind speed derived from its intermittent nature bring a great threat to the wind power production stability, and to the wind turbines themselves. Lately, much work has been done on developing models to forecast average wind speed values, yet surprisingly little has focused on proposing models to accurately forecast extreme wind speeds, which can damage the turbines. In this work, we develop a flexible spliced Gamma-Generalized Pareto model to forecast extreme and non-extreme wind speeds simultaneously. Our model belongs to the class of latent Gaussian models, for which inference is conveniently performed based on the integrated nested Laplace approximation method. Considering a flexible additive regression structure, we propose two models for the latent linear predictor to capture the spatio-temporal dynamics of wind speeds. Our models are fast to fit and can describe both the bulk and the tail of the wind speed distribution while producing short-term extreme and non-extreme wind speed probabilistic forecasts.Comment: 25 page