Nonlinear Multivariate Spatial Modeling Using NLPCA and Pair‐Copulas

A novel geostatistical modeling approach is developed to model nonlinear multivariate spatial dependence using nonlinear principal component analysis (NLPCA) and pair‐copulas. In spatial studies, multivariate measurements are frequently collected at each location. The dependence between such measurements can be complex. In this article, a multivariate geostatistical model is developed that can capture both nonlinear spatial dependence across locations and nonlinear dependence between measurements at a particular location. Nonlinear multivariate dependence between spatial variables is removed using NLPCA. Subsequently, a pair‐copula based model is fitted to each transformed variable to model the univariate nonlinear spatial dependencies. NLPCA and pair‐copulas, within the proposed model, are compared with stepwise conditional transformation (SCT) and conventional kriging. The results show that, for the two case studies presented, the proposed model that utilizes NLPCA and pair‐copulas reproduces nonlinear multivariate structures and univariate distributions better than existing methods based on SCT and kriging.     

Sasanian glass from Veh Ardašīr: new evidences by ICP-MS analysis

Forty-seven glass fragments excavated at Veh Ardašīr, in central Iraq, were analysed by ICP-MS, determining 38 chemical elements; the samples represented finished objects as well as waste and raw glass. The obtained data point to the use of sodic plant ash for the production of glass in the entire Sasanian period (third–seventh century AD), strengthening previous results from another set of fragments from the same site. Magnesium and phosphorus contents give further evidence of the possible use of different kinds of plant ash, while trace element levels and some element correlations suggest the recourse to different silica sources. As a whole, the obtained results allow one to recognize three main glass compositions, related to the use of different silica sources combined with different kinds of plant ash. The occurrence of waste and raw glass in all groups of composition confirms that at least glass working took place in Veh Ardašīr.