Bayesian Spatial Homogeneous Regression

For high-dimension spatial regression problems, we propose a effective sparse Bayesian model. By introducing a hierarchical Gaussian Markov random field prior, the model can obtain sparse spatial varying parameters, and meanwhile, it can obtain homogeneous parameters estimation for adjacent spatial regions. We use a fast-converging variational EM algorithm for posterior inference, rather than the traditional sampling-based methods. In the M-step of the algorithm, the optimization can be transformed into a classic adaptive lasso problem by simple deformation. The simulation result demonstrate the better performance of our model both in parameters estimation and variable selection. Finally, the proposed model is used to analyze the impact of the socio-demographic factors on the death rate of the COVID-19 in countries of Europe.