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.     

The Fossil Human from Rabat-Kébibat (Morocco): Comparative Study of the Cranial and Mandibular Fragments

As part of the geological and chronological recontextualization of the Rabat-Kébibat quarry performed by a Franco-Moroccan team of geologists, the human remains discovered in the site and already published were reassessed. The human remains assemblage is composed of 23 cranial fragments, a mandible (including on the right I1, P3, P4, the roots of M1, M2, and M3, and of the left I1, I2, C, P3, P4, and M1), and the left half of the maxillary (including I1, I2, P3, P4, M1, and M2). Through a micro-computerized tomography analysis, the internal structure of the parietal fragment (evaluation of the thickness of the compact table and diploe) and the mandible was examined. Geometric morphometrics were applied on the tridimensional model of the mandible to investigate the conformation of the symphyseal outlines. Results were compared to a large reference collection composed of African, Asiatic, and European hominin fossils, from different chronological range. Our results allow us to clarify the phylogenetic position of the human remains from Rabat-Kebibat, in particular their relationship with other North African hominins.