Approximate Bayesian Inference for Spatial Econometrics Models
Roger S. Bivand, Virgilio Gomez-Rubio, Havard Rue
In this work we explore the use of the Integrated Laplace Approximation (INLA)
for Bayesian inference in some widely used models in Spatial Econometrics.
Bayesian inference often relies on very computationally intensive simulation
methods, such as Markov Chain Monte Carlo. However, when only marginal
inference is needed, INLA provides a fast and accurate estimate of the
posterior marginals of the parameters in the model.
We have compared the results provided by these Spatial Econometrics models to
those obtained with a more general class of Generalized Linear Models with
random effects. In these models, spatial autocorrelation is modelled by means
of correlated Gaussian random effects.
We also discuss a procedure to extend the class of models that the R-INLA
software can fit. This approach is based on conditioning on (i.e., fixing) one
or more parameters so that the resulting models can be fitted with R-INLA. By
repeating this for different values of the fixed parameters we can use
Bayesian Model Average methods to provide the posterior marginal of the
parameters of interest. This is particularly interesting to fit models with
complex spatial autocorrelation structures.
Finally, we discuss the use of all these models on two data sets based on
housing prices in Boston and the probability of business re-opening in New
Orleans in the aftermath of hurricane Katrina.