A Comparison of Models and Methods for Spatial Interpolation in Statistics and Numerical Analysis

摘要: Interpolation of spatial data is a very general mathematical problem with many applications, such as surface reconstruction, the numerical solution partial differential equations, learning theory, and prediction environmental variables, to name few. One important statistical approach this known Kriging, geostatistical term for optimal linear processes. It identical method called kernel interpolation used in analysis same problem, but derived under completely different modelling assumptions. Despite their similarity, these two approaches have so far been developed largely independently within communities.Synthesizing results from both literature new results, monograph presents contrasts paradigms, yielding an understanding notions optimality concepts quantify error. New are presented which allow comprehensive characterization sample path regularity second-order random fields (the common model geostatistics), showing that typical assumptions also made implicitly model. Finally we explore theoretically simulation studies how methods identifying covariance parameters field selecting good can be respective other framework.This PhD thesis entirely self-contained providing concise introduction probability theory reproducing Hilbert spaces. addressed researchers, lectures students background interest either statistics or may serve lecture note well reference manual questions concerning models interpolation.