Spatiotemporal Bayesian Regression

Abstract

In spatial statistics, spatial regression methods are often used to quantify the relative influence of factors on health and crime, among others. Spatial Lag Model (SLM) and Spatial Error Model (SEM) are widely adopted in spatial regression analysis. However, these models assume that dependent variables are continuous and normally distributed and require that parameters must be non-random variables. These assumptions limit the processing or analysis of some spatial information systematically. As opposed to this, a Bayesian spatial regression model treats data as fixed and unknown quantities or parameters as random variables expressed in terms of probabilities. Thus, it can leverage information on the adjacent regions to estimate the dependent variables, overcoming the data sparseness and small-area problem that spatial analysis often encounters. This approach also makes the estimation of model parameters more stable. In spatial statistics, spatial regression methods are often used to quantify the relative influence of factors on health and crime, among others. Spatial Lag Model (SLM) and Spatial Error Model (SEM) are widely adopted in spatial regression analysis. However, these models assume that dependent variables are continuous and normally distributed and require that parameters be non-random variables. These assumptions limit the processing or analysis of some spatial information systematically. As opposed to this, a Bayesian spatial regression model treats data as fixed and unknown quantities or parameters as random variables expressed in terms of probabilities. Thus, it can leverage information on the adjacent regions to estimate the dependent variables, overcoming the data sparseness and small-area problem that spatial analysis often encounters. This approach also makes the estimation of model parameters more stable.