Spatial statistics for complex and object data

Alessandra Menafoglio e Simone Vantini

MOX - Dipartimento di Matematica, Politecnico di Milano

Friday 13th May 2016

15:30:00

Aula Seminari III Piano Edificio 14 - Dipartimento di Matematica, Politecnico di Milano

This talk is the first one of a series of seminars focusing on the analysis of complex data with spatial and/or temporal dependence. Firstly, Alessandra Menafoglio will introduce Object Oriented Geostatistics as a new branch of spatial statistics addressing the problem of analyzing georeferenced complex observations, in the form of high- or infinite-dimensional data, possibly heterogeneous and constrained. For instance, sedimentological and/or geochemical observations are routinely available in the form of functional (e.g., curves, surfaces or images) or distributional data (e.g., cumulative distribution or probability density functions). All these diverse types of information are treated within a unifying framework, by considering the available observations as “object” data. Object-Oriented Kriging and stochastic simulation will be introduced, relying upon a flexible geostatistical methodology able to treat infinite-dimensional data provided that these can be embedded into an appropriate space of objects (i.e., a Hilbert space). The latter should properly capture all the relevant data features through its geometry. Motivated by real case studies, particular emphasis will be given to the problem of prediction (i.e., Kriging) and uncertainty assessment (via stochastic simulation) of distributional data, interpreted as points within the Hilbert space of functional compositions, endowed with the Aitchison geometry. In the second part of the seminar, Simone Vantini will introduce a general non parametric framework for the analysis of complex data with spatial dependence based on random Voronoi tessellations of the area of investigation (i.e., Bagging Voronoi Analysis). In detail, the approach will be presented in connection to a real application dealing with the analysis of varved (annually laminated) sediment data from lake Kassjon in Northern Sweden. These data will be considered as an (6400-year long) instance of sequentially dependent functional data possibly clustered and misaligned. The general framework will be thus displayed in an algorithm named Bagging Voronoi K-Medoid Alignment. A comparison with simpler approaches will be also presented. This latter comparison will show the importance of jointly dealing with clustering, misalignment, and dependence while inferring on past environmental and climate changes from this kind of data. contact: laura.sangalli@polimi.it