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The INLA package provides a tool for computationally efficient Bayesian modeling and inference for various widely used models, more formally the class of latent Gaussian models. It is a non-sampling based framework which provides approximate results for Bayesian inference, using sparse matrices. The swift uptake of this framework for Bayesian modeling is rooted in the computational efficiency of the approach and catalyzed by the demand presented by the big data era. In this paper, we present new developments within the INLA package with the aim to provide a computationally efficient mechanism for the Bayesian inference of relevant challenging situations.

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.

The principles behind the interface to continuous domain spatial models in the R- INLA software package for R are described. The integrated nested Laplace approximation (INLA) approach proposed by Rue, Martino, and Chopin (2009) is a computationally effective alternative to MCMC for Bayesian inference. INLA is designed for latent Gaussian models, a very wide and flexible class of models ranging from (generalized) linear mixed to spatial and spatio-temporal models. Combined with the stochastic partial differential equation approach (SPDE, Lindgren, Rue, and Lindstrm 2011), one can accommodate all kinds of geographically referenced data, including areal and geostatistical ones, as well as spatial point process data. The implementation interface covers stationary spatial mod- els, non-stationary spatial models, and also spatio-temporal models, and is applicable in epidemiology, ecology, environmental risk assessment, as well as general geostatistics.

The integrated nested Laplace approximation (INLA) provides an interesting way of approximating the posterior marginals of a wide range of Bayesian hierarchical models. This approximation is based on conducting a Laplace approximation of certain functions and numerical integration is extensively used to integrate some of the models parameters out. The R-INLA package offers an interface to INLA, providing a suitable framework for data analysis. Although the INLA methodology can deal with a large number of models, only the most relevant have been implemented within R-INLA. However, many other important models are not available for R-INLA yet. In this paper we show how to fit a number of spatial models with R-INLA, including its interaction with other R packages for data analysis. Secondly, we describe a novel method to extend the number of latent models available for the model parameters. Our approach is based on conditioning on one or several model parameters and fit these conditioned models with R-INLA. Then these models are combined using Bayesian model averaging to provide the final approximations to the posterior marginals of the model. Finally, we show some examples of the application of this technique in spatial statistics. It is worth noting that our approach can be extended to a number of other fields, and not only spatial statistics.