  Spatial concurrent linear models, in which the model coefficients are spatial
processes varying at a local level, are flexible and useful tools for analyzing
spatial data. One approach places stationary Gaussian process priors on the
spatial processes, but in applications the data may display strong
nonstationary patterns. In this article, we propose a Bayesian variable
selection approach based on wavelet tools to address this problem. The proposed
approach does not involve any stationarity assumptions on the priors, and
instead we impose a mixture prior directly on each wavelet coefficient. We
introduce an option to control the priors such that high resolution
coefficients are more likely to be zero. Computationally efficient MCMC
procedures are provided to address posterior sampling, and uncertainty in the
estimation is assessed through posterior means and standard deviations.
Examples based on simulated data demonstrate the estimation accuracy and
advantages of the proposed method. We also illustrate the performance of the
proposed method for real data obtained through remote sensing.
