Flexible shrinkage in high-dimensional Bayesian spatial autoregressive models

TL;DR

This paper proposes new global-local shrinkage priors for high-dimensional Bayesian spatial autoregressive models, offering a flexible, efficient alternative to computationally intensive Bayesian model-averaging methods.

Contribution

Introduction of two novel continuous shrinkage priors that facilitate stochastic variable selection in high-dimensional spatial models with efficient MCMC implementation.

Findings

Shrinkage priors perform well in high-dimensional settings.

Methods outperform traditional approaches when parameters exceed observations.

Empirical application demonstrates practical utility in regional economic data.

Abstract

This article introduces two absolutely continuous global-local shrinkage priors to enable stochastic variable selection in the context of high-dimensional matrix exponential spatial specifications. Existing approaches as a means to dealing with overparameterization problems in spatial autoregressive specifications typically rely on computationally demanding Bayesian model-averaging techniques. The proposed shrinkage priors can be implemented using Markov chain Monte Carlo methods in a flexible and efficient way. A simulation study is conducted to evaluate the performance of each of the shrinkage priors. Results suggest that they perform particularly well in high-dimensional environments, especially when the number of parameters to estimate exceeds the number of observations. For an empirical illustration we use pan-European regional economic growth data.