B1255
Title: Blind source separation for non-stationary random fields
Authors: Christoph Muehlmann - Technical University of Vienna (Austria)
Klaus Nordhausen - University of Helsinki (Finland) [presenting]
Francois Bachoc - Universite Paul Sabatier (France)
Abstract: Multivariate spatial data possess many challenges in proper statistical modelling. Firstly, dependencies need to be modelled not only on-sight but as a function of spatial separation. Secondly, as the data is multivariate cross-dependencies need to be considered as well. Usually, this is done in terms of a cross-covariance function, where the multivariate random field is supposed to fulfil second-order stationarity assumptions. Spatial Blind Source Separation (SBSS) is a recently introduced unsupervised statistical tool, which is designed to deal with the challenges of multivariate covariance modelling. In the SBSS model, it is assumed that the observable random field is formed by a latent variable linear mixture, where the latent random field is formed by uncorrelated, weakly stationary random fields. However, second-order stationarity might be too restricting when for example the spatial domain increases and the on-sight variances vary in space, or the spatial covariance actually depends on the locations themselves rather than the distances between them. This leads to non-stationary spatial modeling which again possesses the same challenges as described above and additionally opens the door for a variety of second-order stationary violations. We address these issues by combining the principles of Blind Source Separation and non-stationary geostatistics which leads to Spatial Non-stationary Source Separation (SNSS).
