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Applications Of Independent And Identically Distributed (Iid) Random Processes In Polarimetry And Climatology, Dan Kestner

Dissertations, Master's Theses and Master's Reports

The unifying theme of this thesis is the characterization of “perfect randomness,” i.e., independent and identically distributed (IID) stochastic processes as these are applied in physical science. Two specific and mathematically distinct applications are chosen: (i) Radar and optical polarimetry; (ii) Analysis of time series in meteorology. In (i), IID process of a special kind, namely, with a distribution defined by symmetry, is used to link its multivariate Gaussian density to uniformity on the Poincaré sphere. This “statistical ellipsometry” approach is then used to relate polarimetric mismatches or imbalances to ellipsometric variables and suitably chosen cross-correlation measures. In (ii), recently …