Estimating Spatial Changes Over Time of Arctic Sea Ice using Hidden 2x2 Tables

Arctic sea ice extent has been of considerable interest to scientists in recent years, mainly due to its decreasing temporal trend over the past 20 years. In this article, we propose a hierarchical spatio-temporal generalized linear model for binary Arctic sea-ice-extent data, where statistical dependencies in the data are modeled through a latent spatio-temporal linear mixed effects model. By using a fixed number of spatial basis functions, the resulting model achieves both dimension reduction and non-stationarity for spatial fields at different time points. An EM algorithm is proposed to estimate model parameters, and an empirical-hierarchical-modeling approach is applied to obtain the predictive distribution of the latent spatio-temporal process. We illustrate the accuracy of the parameter estimation through a simulation study. The hierarchical model is applied to spatial Arctic sea-ice-extent data in the month of September for 20 years in the recent past, where several posterior summaries are obtained to detect the changes of Arctic sea ice cover. In particular, we consider a time series of latent 2 x 2 tables to infer the spatial changes of Arctic sea ice over time.