New Frontiers in Bayesian Modeling Using the INLA Package in R

Abstract

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.

Software for Bayesian Statistics

“…Alternatively, other papers (e.g., Corradin et al 2021;Hosszejni and Kastner 2021;Knaus et al 2021;Venturini and Piccarreta 2021) write sampling functions in C++ which are then integrated into R by using the Rcpp (Eddelbuettel and François 2011) and RcppArmadillo (Eddelbuettel and Sanderson 2014) packages. Finally, some papers do not use MCMC but numerical approximations such as Eggleston et al (2021), Fasiolo et al (2021 and Van Niekerk et al (2021). Two papers (Kuschnig and Vashold 2021;Weber et al 2021) also implement priors for specific Bayesian models.…”

“…The special issue includes a number of packages for fitting Bayesian hierarchical models using different types of software. Van Niekerk, Bakka, Rue, and Schenk (2021) present new developments for the INLA package (Lindgren and Rue 2015) about complex joint survival models, non-separable space-time models and high performance computing to fit very large models faster. Similarly, Michaud, De Valpine, Turek, Paciorek, and Nguyen (2021) describe the implementation of algorithms for state-space model analysis using sequential Monte Carlo methods for the nimble software which have been included in the nimbleSMC package.…”

Joint Posterior Inference for Latent Gaussian Models with R-INLA

“…As similar as it may appear, the approximation in (39) does not carry the same accuracy as the posterior marginals π(x i |y) since it lacks a Laplace approximation step. The mixture structure of (39) easily allow to achieve an approximation to the true density in (1) by using a sampling Monte Carlo approach on the pre-computed grid points of the hyperparameter space, as a result of the internal joint approximations obtained in (8).…”

“…The new Skew Gaussian Copula class turns out to be the key role for both computing and improving the joint posterior approximation in (39). We can always get samples from this multivariate density no matter the model to fit, and we can do it fast.…”

“…Bayesian inference for latent Gaussian models (LGMs) have been made more attainable for high dimension and/or complex hierarchical models by the introduction of the Integrated Nested Laplace Approximation (INLA) method proposed by Rue et al (2009). Henceforth this methodology has been used extensively in various fields and modeling applications, see amongst others: health data applications in [1,16,37]; spline models applied in medicine in [3] or spatial/spatio-temporal models in [4,9,10,41,24,21,25]; measurement error model in [22]; modelling applications in [28,6,38] and air data in [5]; a functional data analysis in [42] and time trends for related populations in [29,30]; environmental data applications in [13] and [14] with some genetics in [12]; dynamic and stochastic volatility models respectively in [35,17]; joint models and survival applications in [18,39,36]. It is clear that the advancement made by INLA in the field of deterministic (not sampling-based) Bayesian inference, holds significant impact in science as a whole.…”