An Application of Bayesian Variable Selection to Spatial Concurrent Linear Models

TL;DR

This paper introduces a Bayesian wavelet-based variable selection method for spatial concurrent linear models, effectively handling nonstationary spatial data without stationarity assumptions, and demonstrates its accuracy through simulations and remote sensing data.

Contribution

It proposes a novel Bayesian wavelet approach for spatial models that relaxes stationarity assumptions and improves variable selection in nonstationary spatial data.

Findings

Accurate estimation demonstrated on simulated data.

Method effectively handles nonstationary spatial patterns.

Successful application to remote sensing data.

Abstract

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.