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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 flexibledoi:10.1016/j.spasta.2018.10.004 fatcat:wluk5wvu6jcynjb63n6wqojsjy