Design and Analysis of an Effective Multi-Barriers Model Based on Non-Stationary Gaussian Random Fields

Abstract

In this paper, we propose an extension to the barrier model, i.e., the Multi-Barriers Model, which could characterize an area of interest with different types of obstacles. In the proposed model, the area of interest is divided into two or more areas, which include a general area of interest with sampling points and the rest of the area with different types of obstacles. Firstly, the correlation between the points in space is characterized by the obstruction degree of the obstacle. Secondly, multiple Gaussian random fields are constructed. Then, continuous Gaussian fields are expressed by using stochastic partial differential equations (SPDEs). Finally, the integrated nested Laplace approximation (INLA) method is employed to calculate the posterior mean of parameters and the posterior parameters to establish a spatial regression model. In this paper, the Multi-Barriers Model is also verified by using the geostatistical model and log-Gaussian Cox model. Furthermore, the stationary Gaussian model, the barrier model and the Multi-Barriers Model are investigated in the geostatistical data, respectively. Real data sets of burglaries in a certain area are used to compare the performance of the stationary Gaussian model, barrier model and Multi-Barriers Model. The comparison results suggest that the three models achieve similar performance in the posterior mean and posterior distribution of the parameters, as well as the deviance information criteria (DIC) value. However, the Multi-Barriers Model can better interpret the spatial model established based on the spatial data of the research areas with multiple types of obstacles, and it is closer to reality.