Bayesian Influence Analysis of the Skew-Normal Spatial Autoregression Models

In spatial data analysis, outliers or influential observations have a considerable influence on statistical inference. This paper develops Bayesian influence analysis, including the local influence approach and case influence measures in skew-normal spatial autoregression models (SSARMs). The Bayesian local influence method is proposed to evaluate the impact of small perturbations in data, the distribution of sampling and prior. To measure the extent of different perturbations in SSARMs, the Bayes factor, the phi-divergence and the posterior mean distance are established. A Bayesian case influence measure is presented to examine the influence points in SSARMs. The potential influence points in the models are identified by Cook's posterior mean distance and Cook's posterior mode distance phi-divergence. The Bayesian influence analysis formulation of spatial data is given. Simulation studies and examples verify the effectiveness of the presented methodologies.

Automated summary

This paper develops Bayesian influence analysis methods for spatial data analysis, including local influence method and case influence measures. The impact of small perturbations in data, sampling, and prior is evaluated using Bayesian local influence method, and measures such as Bayes factor, phi-divergence, and posterior mean distance are established to quantify different perturbations in skew-normal spatial autoregression models. A Bayesian case influence measure is presented to examine the influence points in these models. The potential influence points are identified using Cook's posterior mean distance and Cook's posterior mode distance phi-divergence. The effectiveness of the presented methodologies is verified through simulation studies and examples.