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

Computer model calibration with large non-stationary spatial outputs: application to the calibration of a climate model

Bayesian calibration of computer models tunes unknown input parameters by comparing outputs with observations. For model outputs that are distributed over space, this becomes computationally expensive because of the output size. To overcome this challenge, we employ a basis representation of the model outputs and observations: we match these decompositions to carry out the calibration efficiently. In the second step, we incorporate the non-stationary behaviour, in terms of spatial variations of both variance and correlations, in the calibration. We insert two integrated nested Laplace approximation-stochastic partial differential equation parameters into the calibration. A synthetic example and a climate model illustration highlight the benefits of our approach

The Integrated nested Laplace approximation for fitting models with multivariate response

This paper introduces a Laplace approximation to Bayesian inference in regression models for multivariate response variables. We focus on Dirichlet regression models, which can be used to analyze a set of variables on a simplex exhibiting skewness and heteroscedasticity, without having to transform the data. These data, which mainly consist of proportions or percentages of disjoint categories, are widely known as compositional data and are common in areas such as ecology, geology, and psychology. We provide both the theoretical foundations and a description of how this Laplace approximation can be implemented in the case of Dirichlet regression. The paper also introduces the package dirinla in the R-language that extends the INLA package, which can not deal directly with multivariate likelihoods like the Dirichlet likelihood. Simulation studies are presented to validate the good behaviour of the proposed method, while a real data case-study is used to show how this approach can be applied

Designing Proposal Distributions for Particle Filters using Integrated Nested Laplace Approximation

State-space models are used to describe and analyse dynamical systems. They are ubiquitously used in many scientific fields such as signal processing, finance and ecology to name a few. Particle filters are popular inferential methods used for state-space methods. Integrated Nested Laplace Approximation (INLA), an approximate Bayesian inference method, can also be used for this kind of models in case the transition distribution is Gaussian. We present a way to use this framework in order to approximate the particle filter's proposal distribution that incorporates information about the observations, parameters and the previous latent variables. Further, we demonstrate the performance of this proposal on data simulated from a Poisson state-space model used for count data. We also show how INLA can be used to estimate the parameters of certain state-space models (a task that is often challenging) that would be used for Sequential Monte Carlo algorithms.Comment: 13 pages, 4 figure