Estimating Spatial Econometrics Models with Integrated Nested Laplace Approximation

Integrated Nested Laplace Approximation provides a fast and effective method for marginal inference on Bayesian hierarchical models. This methodology has been implemented in the R-INLA package which permits INLA to be used from within R statistical software. Although INLA is implemented as a general methodology, its use in practice is limited to the models implemented in the R-INLA package. Spatial autoregressive models are widely used in spatial econometrics but have until now been missing from the R-INLA package. In this paper, we describe the implementation and application of a new class of latent models in INLA made available through R-INLA. This new latent class implements a standard spatial lag model, which is widely used and that can be used to build more complex models in spatial econometrics. The implementation of this latent model in R-INLA also means that all the other features of INLA can be used for model fitting, model selection and inference in spatial econometrics, as will be shown in this paper. Finally, we will illustrate the use of this new latent model and its applications with two datasets based on Gaussian and binary outcomes

Estimating Animal Abundance with N-Mixture Models Using the R-INLA Package for R

Successful management of wildlife populations requires accurate estimates of abundance. Abundance estimates can be confounded by imperfect detection during wildlife surveys. N-mixture models enable quantification of detection probability and, under appropriate conditions, produce abundance estimates that are less biased. Here, we demonstrate how to use the R-INLA package for R to analyze N-mixture models, and compare performance of R-INLA to two other common approaches: JAGS (via the runjags package for R), which uses Markov chain Monte Carlo and allows Bayesian inference, and the unmarked package for R, which uses maximum likelihood and allows frequentist inference. We show that R-INLA is an attractive option for analyzing N-mixture models when (i) fast computing times are necessary (R-INLA is 10 times faster than unmarked and 500 times faster than JAGS), (ii) familiar model syntax and data format (relative to other R packages) is desired, (iii) survey-level covariates of detection are not essential, and (iv) Bayesian inference is preferred

Bayesian computing with INLA: New features

The INLA approach for approximate Bayesian inference for latent Gaussian models has been shown to give fast and accurate estimates of posterior marginals and also to be a valuable tool in practice via the R-package R-INLA. In this paper we formalize new developments in the R-INLA package and show how these features greatly extend the scope of models that can be analyzed by this interface. We also discuss the current default method in R-INLA to approximate posterior marginals of the hyperparameters using only a modest number of evaluations of the joint posterior distribution of the hyperparameters, without any need for numerical integration

Latent Gaussian modeling and INLA: A review with focus on space-time applications

Bayesian hierarchical models with latent Gaussian layers have proven very flexible in capturing complex stochastic behavior and hierarchical structures in high-dimensional spatial and spatio-temporal data. Whereas simulation-based Bayesian inference through Markov Chain Monte Carlo may be hampered by slow convergence and numerical instabilities, the inferential framework of Integrated Nested Laplace Approximation (INLA) is capable to provide accurate and relatively fast analytical approximations to posterior quantities of interest. It heavily relies on the use of Gauss-Markov dependence structures to avoid the numerical bottleneck of high-dimensional nonsparse matrix computations. With a view towards space-time applications, we here review the principal theoretical concepts, model classes and inference tools within the INLA framework. Important elements to construct space-time models are certain spatial Mat\'ern-like Gauss-Markov random fields, obtained as approximate solutions to a stochastic partial differential equation. Efficient implementation of statistical inference tools for a large variety of models is available through the INLA package of the R software. To showcase the practical use of R-INLA and to illustrate its principal commands and syntax, a comprehensive simulation experiment is presented using simulated non Gaussian space-time count data with a first-order autoregressive dependence structure in time