Bayesian Model Averaging with the Integrated Nested Laplace Approximation

Virgilio Gómez-Rubio,Håvard Rue,Roger S Bivand

doi:10.3390/econometrics8020023

Virgilio Gómez-Rubio, Håvard Rue + Show 1 more

Open Access

https://doi.org/10.3390/econometrics8020023

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Abstract

The integrated nested Laplace approximation (INLA) for Bayesian inference is an efficient approach to estimate the posterior marginal distributions of the parameters and latent effects of Bayesian hierarchical models that can be expressed as latent Gaussian Markov random fields (GMRF). The representation as a GMRF allows the associated software R-INLA to estimate the posterior marginals in a fraction of the time as typical Markov chain Monte Carlo algorithms. INLA can be extended by means of Bayesian model averaging (BMA) to increase the number of models that it can fit to conditional latent GMRF. In this paper, we review the use of BMA with INLA and propose a new example on spatial econometrics models.

Highlights

Bayesian model averaging (BMA; see, for example, Hoeting et al 1999) is a way to combine different Bayesian hierarchical models that can be used to estimate highly parameterized models.By computing an average model, the uncertainty about the model choice is taken into account when estimating the uncertainty of the model parameters.As BMA often requires fitting a large number of models, this can be time consuming when the time required to fit each of the models is large
BMA with integrated nested Laplace approximation (INLA) was a valid approach to make joint posterior inference on a subset of hyperparameters in the model. These results showed the validity of relying on BMA with INLA to fit highly parameterized models
Marginals provided by INLA with maximum likelihood (ML) estimates were very narrow for the fixed effects, which was probably due to ignoring the uncertainty about the spatial autocorrelation parameters

Summary

Introduction

Bayesian model averaging (BMA; see, for example, Hoeting et al 1999) is a way to combine different Bayesian hierarchical models that can be used to estimate highly parameterized models. Gómez-Rubio and Rue (2018) embedded INLA within MCMC so that the joint posterior distribution of a subset of the model parameters is estimated using the Metropolis–Hastings algorithm (Hastings 1970; Metropolis et al 1953). This requires fitting a model with INLA (conditional on some parameters) at each step, so that the resulting models can be combined to obtain the posterior marginals of the remainder of the model parameters. Weights are computed by using Bayes’ rule, and they depend on the marginal likelihood of the conditional model and the prior distribution of the conditioning hyperparameters

Spatial Econometrics Models

The Integrated Nested Laplace Approximation

Bayesian Model Averaging with INLA

Example

Discussion